mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -6,7 +6,7 @@ Authors: Robert Y. Lewis, Keeley Hoek
 import Algebra.NeZero
 import Algebra.Order.WithZero
 import Order.RelIso.Basic
-import Data.Nat.Order.Basic
+import Algebra.Order.Group.Nat
 import Order.Hom.Set
 
 #align_import data.fin.basic from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -682,7 +682,7 @@ theorem coe_orderIso_apply (e : Fin n ≃o Fin m) (i : Fin n) : (e i : ℕ) = i
   induction' i using Nat.strong_induction_on with i h
   refine' le_antisymm (forall_lt_iff_le.1 fun j hj => _) (forall_lt_iff_le.1 fun j hj => _)
   · have := e.symm.lt_iff_lt.2 (mk_lt_of_lt_coe hj)
-    rw [e.symm_apply_apply] at this 
+    rw [e.symm_apply_apply] at this
     convert this
     simpa using h _ this (e.symm _).is_lt
   · rwa [← h j hj (hj.trans hi), ← lt_iff_coe_lt_coe, e.lt_iff_lt]
@@ -912,7 +912,7 @@ theorem mk_bit1 {m n : ℕ} [NeZero n] (h : bit1 m < n) :
       (bit1 ⟨m, (Nat.le_add_right m m).trans_lt ((m + m).lt_succ_self.trans h)⟩ : Fin _) :=
   by
   ext
-  simp only [bit1, bit0] at h 
+  simp only [bit1, bit0] at h
   simp only [bit1, bit0, coe_add, coe_one', coe_mk, ← Nat.add_mod, Nat.mod_eq_of_lt h]
 #align fin.mk_bit1 Fin.mk_bit1
 -/
@@ -1008,7 +1008,7 @@ theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) <
   by
   cases n
   · exact absurd h (Nat.not_lt_zero _)
-  · rw [lt_iff_coe_lt_coe, coe_last, ← add_lt_add_iff_right 1] at h 
+  · rw [lt_iff_coe_lt_coe, coe_last, ← add_lt_add_iff_right 1] at h
     rw [lt_iff_coe_lt_coe, coe_add, coe_zero, coe_one, Nat.mod_eq_of_lt h]
     exact Nat.zero_lt_succ _
 #align fin.add_one_pos Fin.add_one_pos
@@ -1033,7 +1033,7 @@ theorem zero_eq_one_iff [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 :=
   constructor
   · intro h
     have := congr_arg (coe : Fin n → ℕ) h
-    simp only [Fin.val_zero, ← Nat.dvd_iff_mod_eq_zero, Fin.val_one', @eq_comm _ 0] at this 
+    simp only [Fin.val_zero, ← Nat.dvd_iff_mod_eq_zero, Fin.val_one', @eq_comm _ 0] at this
     exact eq_one_of_dvd_one this
   · rintro rfl; rfl
 #align fin.zero_eq_one_iff Fin.zero_eq_one_iff
@@ -2285,7 +2285,7 @@ theorem liftFun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {
   · refine' fun H i => Fin.induction _ _
     · exact fun h => (h.not_le (zero_le i)).elim
     · intro j ihj hij
-      rw [← le_cast_succ_iff] at hij 
+      rw [← le_cast_succ_iff] at hij
       rcases hij.eq_or_lt with (rfl | hlt)
       exacts [H j, trans (ihj hlt) (H j)]
 #align fin.lift_fun_iff_succ Fin.liftFun_iff_succ
@@ -2404,7 +2404,7 @@ theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a
   · simp [h]
   rw [sub_eq_add_neg, coe_add_eq_ite, coe_neg_one, if_pos, add_comm, add_tsub_add_eq_tsub_left]
   rw [add_comm ↑a, add_le_add_iff_left, Nat.one_le_iff_ne_zero]
-  rwa [Fin.ext_iff] at h 
+  rwa [Fin.ext_iff] at h
 #align fin.coe_sub_one Fin.coe_sub_one
 -/
 
@@ -2582,7 +2582,7 @@ theorem succAbove_lt_iff_castSucc_lt (p : Fin (n + 1)) (i : Fin n) :
   · intro h
     cases' succ_above_lt_ge p i with H H
     · exact H
-    · rw [succ_above_above _ _ H] at h 
+    · rw [succ_above_above _ _ H] at h
       exact lt_trans (cast_succ_lt_succ i) h
   · intro h
     rw [succ_above_below _ _ h]
@@ -2599,7 +2599,7 @@ theorem lt_succAbove_iff_le_castSucc (p : Fin (n + 1)) (i : Fin n) :
   refine' Iff.intro _ _
   · intro h
     cases' succ_above_lt_ge p i with H H
-    · rw [succ_above_below _ _ H] at h 
+    · rw [succ_above_below _ _ H] at h
       exact le_of_lt h
     · exact H
   · intro h
@@ -2812,7 +2812,7 @@ theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H
     calc
       _ ≤ _ := Nat.pred_le _
       _ ≤ _ := H
-  · simp at ha ; exact le_pred_of_lt (lt_of_le_of_lt ha hb)
+  · simp at ha; exact le_pred_of_lt (lt_of_le_of_lt ha hb)
   · exact H
 #align fin.pred_above_right_monotone Fin.predAbove_right_monotone
 -/
@@ -2931,7 +2931,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
     -- For some reason `simp` doesn't fire fully unless we discharge the third goal.
     · exact lt_of_le_of_ne H (Ne.symm h)
     · simp
-    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSucc_mk] at h 
+    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSucc_mk] at h
       simp only [pred, Fin.mk_lt_mk, not_lt]
       exact Nat.le_pred_of_lt (Nat.lt_of_le_of_ne H (Ne.symm h))
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
@@ -3006,11 +3006,11 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
       ext
       have h₀ : (b : ℕ) < n + 1 :=
         by
-        simp only [le_iff_coe_le_coe, coe_cast_succ] at h₂ 
+        simp only [le_iff_coe_le_coe, coe_cast_succ] at h₂
         simpa only [lt_succ_iff] using h₂.trans a.is_le
       have h₁ : (b.succ : ℕ) < n + 2 :=
         by
-        rw [← Nat.succ_lt_succ_iff] at h₀ 
+        rw [← Nat.succ_lt_succ_iff] at h₀
         simpa only [coe_succ] using h₀
       simp only [coe_cast_pred b h₀, coe_cast_pred b.succ h₁, coe_succ]
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -94,11 +94,11 @@ def finZeroElim {α : Fin 0 → Sort u} (x : Fin 0) : α x :=
 
 namespace Fin
 
-#print Fin.elim0' /-
+#print Fin.elim0 /-
 /-- A non-dependent variant of `elim0`. -/
-def elim0' {α : Sort _} (x : Fin 0) : α :=
+def elim0 {α : Sort _} (x : Fin 0) : α :=
   x.elim0ₓ
-#align fin.elim0' Fin.elim0'
+#align fin.elim0' Fin.elim0
 -/
 
 variable {n m : ℕ} {a b : Fin n}

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -2494,19 +2494,19 @@ def succAboveEmb (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
 #align fin.succ_above Fin.succAboveEmb
 -/
 
-#print Fin.succAbove_below /-
+#print Fin.succAbove_of_castSucc_lt /-
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
-theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
+theorem succAbove_of_castSucc_lt (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
     p.succAboveEmb i = i.cast_succ := by rw [succ_above]; exact if_pos h
-#align fin.succ_above_below Fin.succAbove_below
+#align fin.succ_above_below Fin.succAbove_of_castSucc_lt
 -/
 
 #print Fin.succAbove_ne_zero_zero /-
 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAboveEmb 0 = 0 :=
   by
-  rw [Fin.succAbove_below]
+  rw [Fin.succAbove_of_castSucc_lt]
   · rfl
   · exact bot_lt_iff_ne_bot.mpr ha
 #align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zero
@@ -2548,12 +2548,12 @@ theorem succAbove_last_apply (i : Fin n) : succAboveEmb (Fin.last n) i = i.cast_
 #align fin.succ_above_last_apply Fin.succAbove_last_apply
 -/
 
-#print Fin.succAbove_above /-
+#print Fin.succAbove_of_le_castSucc /-
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
-theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
+theorem succAbove_of_le_castSucc (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
     p.succAboveEmb i = i.succ := by simp [succ_above, h.not_lt]
-#align fin.succ_above_above Fin.succAbove_above
+#align fin.succ_above_above Fin.succAbove_of_le_castSucc
 -/
 
 #print Fin.succAbove_lt_ge /-
@@ -2571,11 +2571,12 @@ theorem castSucc_lt_or_lt_succ (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p 
 #align fin.succ_above_lt_gt Fin.castSucc_lt_or_lt_succ
 -/
 
-#print Fin.succAbove_lt_iff /-
+#print Fin.succAbove_lt_iff_castSucc_lt /-
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
 @[simp]
-theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAboveEmb i < p ↔ i.cast_succ < p :=
+theorem succAbove_lt_iff_castSucc_lt (p : Fin (n + 1)) (i : Fin n) :
+    p.succAboveEmb i < p ↔ i.cast_succ < p :=
   by
   refine' Iff.intro _ _
   · intro h
@@ -2586,13 +2587,14 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAboveEmb i < p 
   · intro h
     rw [succ_above_below _ _ h]
     exact h
-#align fin.succ_above_lt_iff Fin.succAbove_lt_iff
+#align fin.succ_above_lt_iff Fin.succAbove_lt_iff_castSucc_lt
 -/
 
-#print Fin.lt_succAbove_iff /-
+#print Fin.lt_succAbove_iff_le_castSucc /-
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
-theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAboveEmb i ↔ p ≤ i.cast_succ :=
+theorem lt_succAbove_iff_le_castSucc (p : Fin (n + 1)) (i : Fin n) :
+    p < p.succAboveEmb i ↔ p ≤ i.cast_succ :=
   by
   refine' Iff.intro _ _
   · intro h
@@ -2603,7 +2605,7 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAboveEmb i 
   · intro h
     rw [succ_above_above _ _ h]
     exact lt_of_le_of_lt h (cast_succ_lt_succ i)
-#align fin.lt_succ_above_iff Fin.lt_succAbove_iff
+#align fin.lt_succ_above_iff Fin.lt_succAbove_iff_le_castSucc
 -/
 
 #print Fin.succAbove_ne /-
@@ -2628,32 +2630,30 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
 #align fin.succ_above_pos Fin.succAbove_pos
 -/
 
-#print Fin.succAbove_castLT /-
 @[simp]
-theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
+theorem succAboveEmb_castLT {x y : Fin (n + 1)} (h : x < y)
     (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAboveEmb (x.castLT hx) = x := by
   rw [succ_above_below, cast_succ_cast_lt]; exact h
-#align fin.succ_above_cast_lt Fin.succAbove_castLT
--/
+#align fin.succ_above_cast_lt Fin.succAboveEmb_castLT
 
-#print Fin.succAbove_pred /-
 @[simp]
-theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
-    x.succAboveEmb (y.pred hy) = y := by rw [succ_above_above, succ_pred];
-  simpa [le_iff_coe_le_coe] using Nat.le_pred_of_lt h
-#align fin.succ_above_pred Fin.succAbove_pred
--/
+theorem succAboveEmb_pred {x y : Fin (n + 1)} (h : x < y)
+    (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') : x.succAboveEmb (y.pred hy) = y := by
+  rw [succ_above_above, succ_pred]; simpa [le_iff_coe_le_coe] using Nat.le_pred_of_lt h
+#align fin.succ_above_pred Fin.succAboveEmb_pred
 
-#print Fin.castLT_succAbove /-
-theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSuccEmb x < y)
-    (h' : (y.succAboveEmb x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
+#print Fin.castPred_succAbove /-
+theorem castPred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSuccEmb x < y)
+    (h' : (y.succAboveEmb x).1 < n :=
+      lt_of_lt_of_le ((succAbove_lt_iff_castSucc_lt _ _).2 h) (le_last y)) :
     (y.succAboveEmb x).castLT h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
-#align fin.cast_lt_succ_above Fin.castLT_succAbove
+#align fin.cast_lt_succ_above Fin.castPred_succAbove
 -/
 
 #print Fin.pred_succAbove /-
 theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSuccEmb x)
-    (h' : y.succAboveEmb x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
+    (h' : y.succAboveEmb x ≠ 0 :=
+      (y.zero_le.trans_lt <| (lt_succAbove_iff_le_castSucc _ _).2 h).ne') :
     (y.succAboveEmb x).pred h' = x := by simp only [succ_above_above _ _ h, pred_succ]
 #align fin.pred_succ_above Fin.pred_succAbove
 -/
@@ -2691,11 +2691,11 @@ theorem range_succ (n : ℕ) : Set.range (Fin.succ : Fin n → Fin (n + 1)) = {0
 #align fin.range_succ Fin.range_succ
 -/
 
-#print Fin.exists_succ_eq_iff /-
+#print Fin.exists_succ_eq /-
 @[simp]
-theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠ 0 :=
+theorem exists_succ_eq {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠ 0 :=
   @exists_succAbove_eq_iff n 0 x
-#align fin.exists_succ_eq_iff Fin.exists_succ_eq_iff
+#align fin.exists_succ_eq_iff Fin.exists_succ_eq
 -/
 
 #print Fin.succAbove_right_injective /-
@@ -2737,7 +2737,7 @@ theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAboveEmb i
 #print Fin.succ_succAbove_zero /-
 @[simp]
 theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAboveEmb 0 = 0 :=
-  succAbove_below _ _ (succ_pos _)
+  succAbove_of_castSucc_lt _ _ (succ_pos _)
 #align fin.succ_succ_above_zero Fin.succ_succAbove_zero
 -/
 
@@ -2850,14 +2850,14 @@ theorem castPred_one : castPred (1 : Fin (n + 2)) = 1 := by cases n; apply Subsi
 #align fin.cast_pred_one Fin.castPred_one
 -/
 
-#print Fin.predAbove_zero /-
+#print Fin.predAbove_zero_of_ne_zero /-
 @[simp]
-theorem predAbove_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred hi :=
+theorem predAbove_zero_of_ne_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred hi :=
   by
   dsimp [pred_above]
   rw [dif_pos]
   exact (pos_iff_ne_zero _).mpr hi
-#align fin.pred_above_zero Fin.predAbove_zero
+#align fin.pred_above_zero Fin.predAbove_zero_of_ne_zero
 -/
 
 @[simp]
@@ -2884,13 +2884,13 @@ theorem coe_castPred {n : ℕ} (a : Fin (n + 2)) (hx : a < Fin.last _) : (a.cast
 #align fin.coe_cast_pred Fin.coe_castPred
 -/
 
-#print Fin.predAbove_below /-
-theorem predAbove_below (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_succ) :
+#print Fin.predAbove_of_le_castSucc /-
+theorem predAbove_of_le_castSucc (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_succ) :
     p.predAbove i = i.cast_pred :=
   by
   have : i ≤ (last n).cast_succ := h.trans p.le_last
   simp [pred_above, cast_pred, h.not_lt, this.not_lt]
-#align fin.pred_above_below Fin.predAbove_below
+#align fin.pred_above_below Fin.predAbove_of_le_castSucc
 -/
 
 @[simp]
@@ -2904,10 +2904,10 @@ theorem predAbove_last_apply (i : Fin n) : predAbove (Fin.last n) i = i.cast_pre
 #align fin.pred_above_last_apply Fin.predAbove_last_apply
 -/
 
-#print Fin.predAbove_above /-
-theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
+#print Fin.predAbove_of_castSucc_lt /-
+theorem predAbove_of_castSucc_lt (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
     p.predAbove i = i.pred (p.cast_succ.zero_le.trans_lt h).Ne.symm := by simp [pred_above, h]
-#align fin.pred_above_above Fin.predAbove_above
+#align fin.pred_above_above Fin.predAbove_of_castSucc_lt
 -/
 
 theorem castPred_monotone : Monotone (@castPred n) :=
@@ -2975,12 +2975,12 @@ theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (
   by
   obtain hbelow | habove := lt_or_le b.cast_succ a
   -- `rwa` uses them
-  · rw [Fin.succAbove_below]
-    · rwa [cast_succ_pred_eq_pred_cast_succ, Fin.pred_inj, Fin.succAbove_below]
+  · rw [Fin.succAbove_of_castSucc_lt]
+    · rwa [cast_succ_pred_eq_pred_cast_succ, Fin.pred_inj, Fin.succAbove_of_castSucc_lt]
     · rwa [cast_succ_pred_eq_pred_cast_succ, pred_lt_pred_iff]
-  · rw [Fin.succAbove_above]
+  · rw [Fin.succAbove_of_le_castSucc]
     have : (b.pred hb).succ = b.succ.pred (Fin.succ_ne_zero _) := by rw [succ_pred, pred_succ]
-    · rwa [this, Fin.pred_inj, Fin.succAbove_above]
+    · rwa [this, Fin.pred_inj, Fin.succAbove_of_le_castSucc]
     · rwa [cast_succ_pred_eq_pred_cast_succ, Fin.pred_le_pred_iff]
 #align fin.pred_succ_above_pred Fin.pred_succAbove_pred
 -/
@@ -2992,14 +2992,15 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
     a.succ.predAbove b.succ = (a.predAbove b).succ :=
   by
   obtain h₁ | h₂ := lt_or_le a.cast_succ b
-  · rw [Fin.predAbove_above _ _ h₁, Fin.succ_pred, Fin.predAbove_above, Fin.pred_succ]
+  · rw [Fin.predAbove_of_castSucc_lt _ _ h₁, Fin.succ_pred, Fin.predAbove_of_castSucc_lt,
+      Fin.pred_succ]
     simpa only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, add_lt_add_iff_right] using
       h₁
   · cases n
     · exfalso
       exact not_lt_zero' a.is_lt
-    · rw [Fin.predAbove_below a b h₂,
-        Fin.predAbove_below a.succ b.succ
+    · rw [Fin.predAbove_of_le_castSucc a b h₂,
+        Fin.predAbove_of_le_castSucc a.succ b.succ
           (by
             simpa only [le_iff_coe_le_coe, coe_succ, coe_cast_succ, add_le_add_iff_right] using h₂)]
       ext

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1066,37 +1066,37 @@ theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by simp [lt_iff_coe
 #align fin.succ_pos Fin.succ_pos
 -/
 
-#print Fin.succEmbedding /-
+#print Fin.succEmb /-
 /-- `fin.succ` as an `order_embedding` -/
-def succEmbedding (n : ℕ) : Fin n ↪o Fin (n + 1) :=
+def succEmb (n : ℕ) : Fin n ↪o Fin (n + 1) :=
   OrderEmbedding.ofStrictMono Fin.succ fun ⟨i, hi⟩ ⟨j, hj⟩ h => succ_lt_succ h
-#align fin.succ_embedding Fin.succEmbedding
+#align fin.succ_embedding Fin.succEmb
 -/
 
-#print Fin.val_succEmbedding /-
+#print Fin.val_succEmb /-
 @[simp]
-theorem val_succEmbedding : ⇑(succEmbedding n) = Fin.succ :=
+theorem val_succEmb : ⇑(succEmb n) = Fin.succ :=
   rfl
-#align fin.coe_succ_embedding Fin.val_succEmbedding
+#align fin.coe_succ_embedding Fin.val_succEmb
 -/
 
 #print Fin.succ_le_succ_iff /-
 @[simp]
 theorem succ_le_succ_iff : a.succ ≤ b.succ ↔ a ≤ b :=
-  (succEmbedding n).le_iff_le
+  (succEmb n).le_iff_le
 #align fin.succ_le_succ_iff Fin.succ_le_succ_iff
 -/
 
 #print Fin.succ_lt_succ_iff /-
 @[simp]
 theorem succ_lt_succ_iff : a.succ < b.succ ↔ a < b :=
-  (succEmbedding n).lt_iff_lt
+  (succEmb n).lt_iff_lt
 #align fin.succ_lt_succ_iff Fin.succ_lt_succ_iff
 -/
 
 #print Fin.succ_injective /-
 theorem succ_injective (n : ℕ) : Injective (@Fin.succ n) :=
-  (succEmbedding n).Injective
+  (succEmb n).Injective
 #align fin.succ_injective Fin.succ_injective
 -/
 
@@ -2165,7 +2165,7 @@ theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b :=
 #align fin.fin_two_eq_of_eq_zero_iff Fin.fin_two_eq_of_eq_zero_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
+/- ./././Mathport/Syntax/Translate/Command.lean:299:8: warning: using_well_founded used, estimated equivalent -/
 #print Fin.reverseInduction /-
 /--
 Define `C i` by reverse induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
@@ -2184,8 +2184,7 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
         rw [tsub_lt_tsub_iff_left_of_le] <;> simp [*, Nat.succ_le_iff]
       have hi : i = Fin.castSuccEmb j := Fin.ext rfl
       cast (by rw [hi]) (hs _ (reverse_induction j.succ))
-termination_by
-  _ x => WellFounded.wrap (measure_wf fun i : Fin (n + 1) => n + 1 - i) x
+termination_by x => WellFounded.wrap (measure_wf fun i : Fin (n + 1) => n + 1 - i) x
 #align fin.reverse_induction Fin.reverseInduction
 -/
 
@@ -2482,7 +2481,7 @@ section SuccAbove
 #print Fin.strictMono_succAbove /-
 theorem strictMono_succAbove (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
-  (castSuccEmb : Fin n ↪o _).StrictMono.ite (succEmbedding n).StrictMono
+  (castSuccEmb : Fin n ↪o _).StrictMono.ite (succEmb n).StrictMono
     (fun i j hij hj => lt_trans ((castSuccEmb : Fin n ↪o _).lt_iff_lt.2 hij) hj) fun i =>
     (castSucc_lt_succ i).le
 #align fin.succ_above_aux Fin.strictMono_succAbove

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -2564,12 +2564,12 @@ theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p 
 #align fin.succ_above_lt_ge Fin.succAbove_lt_ge
 -/
 
-#print Fin.succAbove_lt_gt /-
+#print Fin.castSucc_lt_or_lt_succ /-
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
-theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
+theorem castSucc_lt_or_lt_succ (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
   Or.cases_on (succAbove_lt_ge p i) (fun h => Or.inl h) fun h =>
     Or.inr (lt_of_le_of_lt h (castSucc_lt_succ i))
-#align fin.succ_above_lt_gt Fin.succAbove_lt_gt
+#align fin.succ_above_lt_gt Fin.castSucc_lt_or_lt_succ
 -/
 
 #print Fin.succAbove_lt_iff /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -2861,12 +2861,10 @@ theorem predAbove_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred
 #align fin.pred_above_zero Fin.predAbove_zero
 -/
 
-#print Fin.castPred_last /-
 @[simp]
 theorem castPred_last : castPred (last (n + 1)) = last n :=
   eq_of_veq (by simp [cast_pred, pred_above, cast_succ_lt_last])
 #align fin.cast_pred_last Fin.castPred_last
--/
 
 #print Fin.castPred_mk /-
 @[simp]
@@ -2896,12 +2894,10 @@ theorem predAbove_below (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_su
 #align fin.pred_above_below Fin.predAbove_below
 -/
 
-#print Fin.predAbove_last /-
 @[simp]
 theorem predAbove_last : predAbove (Fin.last n) = castPred :=
   rfl
 #align fin.pred_above_last Fin.predAbove_last
--/
 
 #print Fin.predAbove_last_apply /-
 theorem predAbove_last_apply (i : Fin n) : predAbove (Fin.last n) i = i.cast_pred := by
@@ -2915,11 +2911,9 @@ theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
 #align fin.pred_above_above Fin.predAbove_above
 -/
 
-#print Fin.castPred_monotone /-
 theorem castPred_monotone : Monotone (@castPred n) :=
   predAbove_right_monotone (last _)
 #align fin.cast_pred_monotone Fin.castPred_monotone
--/
 
 #print Fin.succAbove_predAbove /-
 /-- Sending `fin (n+1)` to `fin n` by subtracting one from anything above `p`
@@ -3038,7 +3032,6 @@ theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSuccEmb i.cas
 #align fin.cast_succ_cast_pred Fin.castSucc_castPred
 -/
 
-#print Fin.coe_castPred_le_self /-
 theorem coe_castPred_le_self (i : Fin (n + 2)) : (i.cast_pred : ℕ) ≤ i :=
   by
   rcases i.le_last.eq_or_lt with (rfl | h)
@@ -3047,9 +3040,7 @@ theorem coe_castPred_le_self (i : Fin (n + 2)) : (i.cast_pred : ℕ) ≤ i :=
     · simp
     · simpa [lt_iff_coe_lt_coe, le_iff_coe_le_coe, lt_succ_iff] using h
 #align fin.coe_cast_pred_le_self Fin.coe_castPred_le_self
--/
 
-#print Fin.coe_castPred_lt_iff /-
 theorem coe_castPred_lt_iff {i : Fin (n + 2)} : (i.cast_pred : ℕ) < i ↔ i = Fin.last _ :=
   by
   rcases i.le_last.eq_or_lt with (rfl | H)
@@ -3058,9 +3049,7 @@ theorem coe_castPred_lt_iff {i : Fin (n + 2)} : (i.cast_pred : ℕ) < i ↔ i =
     rw [← cast_succ_cast_pred H]
     simp
 #align fin.coe_cast_pred_lt_iff Fin.coe_castPred_lt_iff
--/
 
-#print Fin.lt_last_iff_coe_castPred /-
 theorem lt_last_iff_coe_castPred {i : Fin (n + 2)} : i < Fin.last _ ↔ (i.cast_pred : ℕ) = i :=
   by
   rcases i.le_last.eq_or_lt with (rfl | H)
@@ -3069,7 +3058,6 @@ theorem lt_last_iff_coe_castPred {i : Fin (n + 2)} : i < Fin.last _ ↔ (i.cast_
     rw [← cast_succ_cast_pred H]
     simp
 #align fin.lt_last_iff_coe_cast_pred Fin.lt_last_iff_coe_castPred
--/
 
 end PredAbove
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -2165,6 +2165,7 @@ theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b :=
 #align fin.fin_two_eq_of_eq_zero_iff Fin.fin_two_eq_of_eq_zero_iff
 -/
 
+/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
 #print Fin.reverseInduction /-
 /--
 Define `C i` by reverse induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
@@ -2183,7 +2184,8 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
         rw [tsub_lt_tsub_iff_left_of_le] <;> simp [*, Nat.succ_le_iff]
       have hi : i = Fin.castSuccEmb j := Fin.ext rfl
       cast (by rw [hi]) (hs _ (reverse_induction j.succ))
-termination_by' ⟨_, measure_wf fun i : Fin (n + 1) => n + 1 - i⟩
+termination_by
+  _ x => WellFounded.wrap (measure_wf fun i : Fin (n + 1) => n + 1 - i) x
 #align fin.reverse_induction Fin.reverseInduction
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -937,11 +937,11 @@ theorem val_two {n : ℕ} : ((2 : Fin (n + 3)) : ℕ) = 2 :=
 
 section OfNatCoe
 
-#print Fin.ofNat_eq_val /-
+#print Fin.ofNat''_eq_cast /-
 @[simp]
-theorem ofNat_eq_val (n : ℕ) (a : ℕ) : (ofNat a : Fin (n + 1)) = a :=
+theorem ofNat''_eq_cast (n : ℕ) (a : ℕ) : (ofNat a : Fin (n + 1)) = a :=
   rfl
-#align fin.of_nat_eq_coe Fin.ofNat_eq_val
+#align fin.of_nat_eq_coe Fin.ofNat''_eq_cast
 -/
 
 @[simp]
@@ -992,7 +992,7 @@ theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : ((a : ℕ) : Fin n)
 
 #print Fin.cast_nat_eq_last /-
 theorem cast_nat_eq_last (n) : (n : Fin (n + 1)) = Fin.last n := by
-  rw [← Fin.ofNat_eq_val, Fin.ofNat, Fin.last]; simp only [Nat.mod_eq_of_lt n.lt_succ_self]
+  rw [← Fin.ofNat''_eq_cast, Fin.ofNat, Fin.last]; simp only [Nat.mod_eq_of_lt n.lt_succ_self]
 #align fin.coe_nat_eq_last Fin.cast_nat_eq_last
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -2389,7 +2389,7 @@ theorem coe_neg_one : ↑(-1 : Fin (n + 1)) = n :=
   by
   cases n
   · simp
-  rw [Fin.coe_neg, Fin.val_one, Nat.succ_sub_one, Nat.mod_eq_of_lt]
+  rw [Fin.coe_neg, Fin.val_one, Nat.add_one_sub_one, Nat.mod_eq_of_lt]
   constructor
 #align fin.coe_neg_one Fin.coe_neg_one
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -2938,7 +2938,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
     · simp
     · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSucc_mk] at h 
       simp only [pred, Fin.mk_lt_mk, not_lt]
-      exact Nat.le_pred_of_lt (Nat.lt_of_le_and_ne H (Ne.symm h))
+      exact Nat.le_pred_of_lt (Nat.lt_of_le_of_ne H (Ne.symm h))
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,11 +3,11 @@ Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Keeley Hoek
 -/
-import Mathbin.Algebra.NeZero
-import Mathbin.Algebra.Order.WithZero
-import Mathbin.Order.RelIso.Basic
-import Mathbin.Data.Nat.Order.Basic
-import Mathbin.Order.Hom.Set
+import Algebra.NeZero
+import Algebra.Order.WithZero
+import Order.RelIso.Basic
+import Data.Nat.Order.Basic
+import Order.Hom.Set
 
 #align_import data.fin.basic from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

@@ -522,50 +522,44 @@ def revPerm : Equiv.Perm (Fin n) :=
 #align fin.rev Fin.revPerm
 -/
 
-#print Fin.val_revPerm /-
 @[simp]
-theorem val_revPerm (i : Fin n) : (i.revPerm : ℕ) = n - (i + 1) :=
+theorem val_rev (i : Fin n) : (i.revPerm : ℕ) = n - (i + 1) :=
   rfl
-#align fin.coe_rev Fin.val_revPerm
--/
+#align fin.coe_rev Fin.val_revₓ
 
-#print Fin.revPerm_involutive /-
-theorem revPerm_involutive : Involutive (@revPerm n) :=
+#print Fin.rev_involutive /-
+theorem rev_involutive : Involutive (@revPerm n) :=
   Involutive.toPerm_involutive _
-#align fin.rev_involutive Fin.revPerm_involutive
+#align fin.rev_involutive Fin.rev_involutive
 -/
 
-#print Fin.revPerm_injective /-
-theorem revPerm_injective : Injective (@revPerm n) :=
-  revPerm_involutive.Injective
-#align fin.rev_injective Fin.revPerm_injective
+#print Fin.rev_injective /-
+theorem rev_injective : Injective (@revPerm n) :=
+  rev_involutive.Injective
+#align fin.rev_injective Fin.rev_injective
 -/
 
-#print Fin.revPerm_surjective /-
-theorem revPerm_surjective : Surjective (@revPerm n) :=
-  revPerm_involutive.Surjective
-#align fin.rev_surjective Fin.revPerm_surjective
+#print Fin.rev_surjective /-
+theorem rev_surjective : Surjective (@revPerm n) :=
+  rev_involutive.Surjective
+#align fin.rev_surjective Fin.rev_surjective
 -/
 
-#print Fin.revPerm_bijective /-
-theorem revPerm_bijective : Bijective (@revPerm n) :=
-  revPerm_involutive.Bijective
-#align fin.rev_bijective Fin.revPerm_bijective
+#print Fin.rev_bijective /-
+theorem rev_bijective : Bijective (@revPerm n) :=
+  rev_involutive.Bijective
+#align fin.rev_bijective Fin.rev_bijective
 -/
 
-#print Fin.revPerm_inj /-
 @[simp]
-theorem revPerm_inj {i j : Fin n} : i.revPerm = j.revPerm ↔ i = j :=
-  revPerm_injective.eq_iff
-#align fin.rev_inj Fin.revPerm_inj
--/
+theorem rev_inj {i j : Fin n} : i.revPerm = j.revPerm ↔ i = j :=
+  rev_injective.eq_iff
+#align fin.rev_inj Fin.rev_injₓ
 
-#print Fin.revPerm_revPerm /-
 @[simp]
-theorem revPerm_revPerm (i : Fin n) : i.revPerm.revPerm = i :=
-  revPerm_involutive _
-#align fin.rev_rev Fin.revPerm_revPerm
--/
+theorem rev_rev (i : Fin n) : i.revPerm.revPerm = i :=
+  rev_involutive _
+#align fin.rev_rev Fin.rev_revₓ
 
 #print Fin.revPerm_symm /-
 @[simp]
@@ -574,8 +568,7 @@ theorem revPerm_symm : (@revPerm n).symm = revPerm :=
 #align fin.rev_symm Fin.revPerm_symm
 -/
 
-#print Fin.revPerm_eq /-
-theorem revPerm_eq {n a : ℕ} (i : Fin (n + 1)) (h : n = a + i) :
+theorem rev_eq {n a : ℕ} (i : Fin (n + 1)) (h : n = a + i) :
     i.revPerm = ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro h.symm)⟩ :=
   by
   ext
@@ -584,29 +577,24 @@ theorem revPerm_eq {n a : ℕ} (i : Fin (n + 1)) (h : n = a + i) :
     congr
     rw [h]
   rw [add_assoc, add_tsub_cancel_right]
-#align fin.rev_eq Fin.revPerm_eq
--/
+#align fin.rev_eq Fin.rev_eqₓ
 
-#print Fin.revPerm_le_revPerm /-
 @[simp]
-theorem revPerm_le_revPerm {i j : Fin n} : i.revPerm ≤ j.revPerm ↔ j ≤ i := by
+theorem rev_le_rev {i j : Fin n} : i.revPerm ≤ j.revPerm ↔ j ≤ i := by
   simp only [le_iff_coe_le_coe, coe_rev, tsub_le_tsub_iff_left (Nat.add_one_le_iff.2 j.is_lt),
     add_le_add_iff_right]
-#align fin.rev_le_rev Fin.revPerm_le_revPerm
--/
+#align fin.rev_le_rev Fin.rev_le_revₓ
 
-#print Fin.revPerm_lt_revPerm /-
 @[simp]
-theorem revPerm_lt_revPerm {i j : Fin n} : i.revPerm < j.revPerm ↔ j < i :=
-  lt_iff_lt_of_le_iff_le revPerm_le_revPerm
-#align fin.rev_lt_rev Fin.revPerm_lt_revPerm
--/
+theorem rev_lt_rev {i j : Fin n} : i.revPerm < j.revPerm ↔ j < i :=
+  lt_iff_lt_of_le_iff_le rev_le_rev
+#align fin.rev_lt_rev Fin.rev_lt_revₓ
 
 #print Fin.revOrderIso /-
 /-- `fin.rev n` as an order-reversing isomorphism. -/
 @[simps apply toEquiv]
 def revOrderIso {n} : (Fin n)ᵒᵈ ≃o Fin n :=
-  ⟨OrderDual.ofDual.trans revPerm, fun i j => revPerm_le_revPerm⟩
+  ⟨OrderDual.ofDual.trans revPerm, fun i j => rev_le_rev⟩
 #align fin.rev_order_iso Fin.revOrderIso
 -/
 
@@ -1342,47 +1330,39 @@ theorem symm_castIso (h : n = m) : (castIso h).symm = castIso h.symm :=
 #align fin.symm_cast Fin.symm_castIso
 -/
 
-#print Fin.coe_castIso /-
 /-- While `fin.coe_order_iso_apply` is a more general case of this, we mark this `simp` anyway
 as it is eligible for `dsimp`. -/
 @[simp]
-theorem coe_castIso (h : n = m) (i : Fin n) : (castIso h i : ℕ) = i :=
+theorem coe_cast (h : n = m) (i : Fin n) : (castIso h i : ℕ) = i :=
   rfl
-#align fin.coe_cast Fin.coe_castIso
--/
+#align fin.coe_cast Fin.coe_castₓ
 
-#print Fin.castIso_zero /-
+#print Fin.cast_zero /-
 @[simp]
-theorem castIso_zero {n' : ℕ} [NeZero n] {h : n = n'} :
+theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
     castIso h (0 : Fin n) =
       haveI : NeZero n' := by rw [← h] <;> infer_instance
       0 :=
   ext rfl
-#align fin.cast_zero Fin.castIso_zero
+#align fin.cast_zero Fin.cast_zero
 -/
 
-#print Fin.castIso_last /-
 @[simp]
-theorem castIso_last {n' : ℕ} {h : n + 1 = n' + 1} : castIso h (last n) = last n' :=
+theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : castIso h (last n) = last n' :=
   ext (by rw [coe_cast, coe_last, coe_last, Nat.succ_injective h])
-#align fin.cast_last Fin.castIso_last
--/
+#align fin.cast_last Fin.cast_lastₓ
 
-#print Fin.castIso_mk /-
 @[simp]
-theorem castIso_mk (h : n = m) (i : ℕ) (hn : i < n) :
+theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) :
     castIso h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h.le⟩ :=
   rfl
-#align fin.cast_mk Fin.castIso_mk
--/
+#align fin.cast_mk Fin.cast_mkₓ
 
-#print Fin.castIso_trans /-
 @[simp]
-theorem castIso_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
+theorem cast_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
     castIso h' (castIso h i) = castIso (Eq.trans h h') i :=
   rfl
-#align fin.cast_trans Fin.castIso_trans
--/
+#align fin.cast_trans Fin.cast_transₓ
 
 #print Fin.castIso_refl /-
 @[simp]
@@ -1405,12 +1385,12 @@ theorem castIso_to_equiv (h : n = m) : (castIso h).toEquiv = Equiv.cast (h ▸ r
 #align fin.cast_to_equiv Fin.castIso_to_equiv
 -/
 
-#print Fin.castIso_eq_cast /-
+#print Fin.cast_eq_cast /-
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
-theorem castIso_eq_cast (h : n = m) : (castIso h : Fin n → Fin m) = cast (h ▸ rfl) := by subst h;
-  ext; simp
-#align fin.cast_eq_cast Fin.castIso_eq_cast
+theorem cast_eq_cast (h : n = m) : (castIso h : Fin n → Fin m) = cast (h ▸ rfl) := by subst h; ext;
+  simp
+#align fin.cast_eq_cast Fin.cast_eq_cast
 -/
 
 #print Fin.castAddEmb /-
@@ -1427,12 +1407,10 @@ theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAddEmb m i : ℕ) = i :=
 #align fin.coe_cast_add Fin.coe_castAdd
 -/
 
-#print Fin.castAdd_zero /-
 @[simp]
 theorem castAdd_zero : (castAddEmb 0 : Fin n → Fin (n + 0)) = castIso rfl :=
   rfl
-#align fin.cast_add_zero Fin.castAdd_zero
--/
+#align fin.cast_add_zero Fin.castAdd_zeroₓ
 
 #print Fin.castAdd_lt /-
 theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAddEmb n i : ℕ) < m :=
@@ -1462,28 +1440,22 @@ theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAddEmb m i) (castAdd_
 #align fin.cast_lt_cast_add Fin.castLT_castAdd
 -/
 
-#print Fin.castAdd_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
-theorem castAdd_castIso {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
+theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
     castAddEmb m (Fin.castIso h i) = Fin.castIso (congr_arg _ h) (castAddEmb m i) :=
   ext rfl
-#align fin.cast_add_cast Fin.castAdd_castIso
--/
+#align fin.cast_add_cast Fin.castAdd_castₓ
 
-#print Fin.castIso_castAdd_left /-
-theorem castIso_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
+theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     castIso h (castAddEmb m i) = castAddEmb m (castIso (add_right_cancel h) i) :=
   ext rfl
-#align fin.cast_cast_add_left Fin.castIso_castAdd_left
--/
+#align fin.cast_cast_add_left Fin.cast_castAdd_leftₓ
 
-#print Fin.castIso_castAdd_right /-
 @[simp]
-theorem castIso_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
+theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
     castIso h (castAddEmb m' i) = castAddEmb m i :=
   ext rfl
-#align fin.cast_cast_add_right Fin.castIso_castAdd_right
--/
+#align fin.cast_cast_add_right Fin.cast_castAdd_rightₓ
 
 #print Fin.castAdd_castAdd /-
 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
@@ -1492,22 +1464,18 @@ theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
 #align fin.cast_add_cast_add Fin.castAdd_castAdd
 -/
 
-#print Fin.castIso_succ_eq /-
 /-- The cast of the successor is the succesor of the cast. See `fin.succ_cast_eq` for rewriting in
 the reverse direction. -/
 @[simp]
-theorem castIso_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
+theorem cast_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
     castIso h i.succ = (castIso (Nat.succ.inj h) i).succ :=
   ext <| by simp
-#align fin.cast_succ_eq Fin.castIso_succ_eq
--/
+#align fin.cast_succ_eq Fin.cast_succ_eqₓ
 
-#print Fin.succ_castIso_eq /-
-theorem succ_castIso_eq {n' : ℕ} (i : Fin n) (h : n = n') :
+theorem succ_cast_eq {n' : ℕ} (i : Fin n) (h : n = n') :
     (castIso h i).succ = castIso (by rw [h]) i.succ :=
   ext <| by simp
-#align fin.succ_cast_eq Fin.succ_castIso_eq
--/
+#align fin.succ_cast_eq Fin.succ_cast_eqₓ
 
 #print Fin.castSuccEmb /-
 /-- `cast_succ i` embeds `i : fin n` in `fin (n+1)`. -/
@@ -1530,13 +1498,11 @@ theorem castSucc_mk (n i : ℕ) (h : i < n) : castSuccEmb ⟨i, h⟩ = ⟨i, Nat
 #align fin.cast_succ_mk Fin.castSucc_mk
 -/
 
-#print Fin.castIso_castSucc /-
 @[simp]
-theorem castIso_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
+theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
     castIso h (castSuccEmb i) = castSuccEmb (castIso (Nat.succ_injective h) i) := by ext;
   simp only [coe_cast, coe_cast_succ]
-#align fin.cast_cast_succ Fin.castIso_castSucc
--/
+#align fin.cast_cast_succ Fin.cast_castSuccₓ
 
 #print Fin.castSucc_lt_succ /-
 theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
@@ -1733,36 +1699,28 @@ theorem addNat_mk (n i : ℕ) (hi : i < m) : addNatEmb n ⟨i, hi⟩ = ⟨i + n,
 #align fin.add_nat_mk Fin.addNat_mk
 -/
 
-#print Fin.castIso_addNat_zero /-
 @[simp]
-theorem castIso_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
+theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
     castIso h (addNatEmb 0 i) = castIso ((add_zero _).symm.trans h) i :=
   ext <| add_zero _
-#align fin.cast_add_nat_zero Fin.castIso_addNat_zero
--/
+#align fin.cast_add_nat_zero Fin.cast_addNat_zeroₓ
 
-#print Fin.addNat_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
-theorem addNat_castIso {n n' m : ℕ} (i : Fin n') (h : n' = n) :
+theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
     addNatEmb m (castIso h i) = castIso (congr_arg _ h) (addNatEmb m i) :=
   ext rfl
-#align fin.add_nat_cast Fin.addNat_castIso
--/
+#align fin.add_nat_cast Fin.addNat_castₓ
 
-#print Fin.castIso_addNat_left /-
-theorem castIso_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
+theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     castIso h (addNatEmb m i) = addNatEmb m (castIso (add_right_cancel h) i) :=
   ext rfl
-#align fin.cast_add_nat_left Fin.castIso_addNat_left
--/
+#align fin.cast_add_nat_left Fin.cast_addNat_leftₓ
 
-#print Fin.castIso_addNat_right /-
 @[simp]
-theorem castIso_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
+theorem cast_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
     castIso h (addNatEmb m' i) = addNatEmb m i :=
   ext <| (congr_arg ((· + ·) (i : ℕ)) (add_left_cancel h) : _)
-#align fin.cast_add_nat_right Fin.castIso_addNat_right
--/
+#align fin.cast_add_nat_right Fin.cast_addNat_rightₓ
 
 #print Fin.natAddEmb /-
 /-- `nat_add n i` adds `n` to `i` "on the left". -/
@@ -1792,79 +1750,59 @@ theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAddEmb m i :=
 #align fin.le_coe_nat_add Fin.le_coe_natAdd
 -/
 
-#print Fin.natAdd_zero /-
 theorem natAdd_zero {n : ℕ} : Fin.natAddEmb 0 = (Fin.castIso (zero_add n).symm).toRelEmbedding := by
   ext; apply zero_add
-#align fin.nat_add_zero Fin.natAdd_zero
--/
+#align fin.nat_add_zero Fin.natAdd_zeroₓ
 
-#print Fin.natAdd_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
-theorem natAdd_castIso {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
+theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
     natAddEmb m (castIso h i) = castIso (congr_arg _ h) (natAddEmb m i) :=
   ext rfl
-#align fin.nat_add_cast Fin.natAdd_castIso
--/
+#align fin.nat_add_cast Fin.natAdd_castₓ
 
-#print Fin.castIso_natAdd_right /-
-theorem castIso_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
+theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
     castIso h (natAddEmb m i) = natAddEmb m (castIso (add_left_cancel h) i) :=
   ext rfl
-#align fin.cast_nat_add_right Fin.castIso_natAdd_right
--/
+#align fin.cast_nat_add_right Fin.cast_natAdd_rightₓ
 
-#print Fin.castIso_natAdd_left /-
 @[simp]
-theorem castIso_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
+theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
     castIso h (natAddEmb m' i) = natAddEmb m i :=
   ext <| (congr_arg (· + (i : ℕ)) (add_right_cancel h) : _)
-#align fin.cast_nat_add_left Fin.castIso_natAdd_left
--/
+#align fin.cast_nat_add_left Fin.cast_natAdd_leftₓ
 
-#print Fin.castAdd_natAdd /-
 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     castAddEmb p (natAddEmb m i) = castIso (add_assoc _ _ _).symm (natAddEmb m (castAddEmb p i)) :=
   ext rfl
-#align fin.cast_add_nat_add Fin.castAdd_natAdd
--/
+#align fin.cast_add_nat_add Fin.castAdd_natAddₓ
 
-#print Fin.natAdd_castAdd /-
 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     natAddEmb m (castAddEmb p i) = castIso (add_assoc _ _ _) (castAddEmb p (natAddEmb m i)) :=
   ext rfl
-#align fin.nat_add_cast_add Fin.natAdd_castAdd
--/
+#align fin.nat_add_cast_add Fin.natAdd_castAddₓ
 
-#print Fin.natAdd_natAdd /-
 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
     natAddEmb m (natAddEmb n i) = castIso (add_assoc _ _ _) (natAddEmb (m + n) i) :=
   ext <| (add_assoc _ _ _).symm
-#align fin.nat_add_nat_add Fin.natAdd_natAdd
--/
+#align fin.nat_add_nat_add Fin.natAdd_natAddₓ
 
-#print Fin.castIso_natAdd_zero /-
 @[simp]
-theorem castIso_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
+theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
     castIso h (natAddEmb 0 i) = castIso ((zero_add _).symm.trans h) i :=
   ext <| zero_add _
-#align fin.cast_nat_add_zero Fin.castIso_natAdd_zero
--/
+#align fin.cast_nat_add_zero Fin.cast_natAdd_zeroₓ
 
-#print Fin.castIso_natAdd /-
 @[simp]
-theorem castIso_natAdd (n : ℕ) {m : ℕ} (i : Fin m) :
+theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) :
     castIso (add_comm _ _) (natAddEmb n i) = addNatEmb n i :=
   ext <| add_comm _ _
-#align fin.cast_nat_add Fin.castIso_natAdd
--/
+#align fin.cast_nat_add Fin.cast_natAddₓ
 
-#print Fin.castIso_addNat /-
 @[simp]
-theorem castIso_addNat {n : ℕ} (m : ℕ) (i : Fin n) :
+theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) :
     castIso (add_comm _ _) (addNatEmb m i) = natAddEmb m i :=
   ext <| add_comm _ _
-#align fin.cast_add_nat Fin.castIso_addNat
--/
+#align fin.cast_add_nat Fin.cast_addNatₓ
 
 #print Fin.natAdd_last /-
 @[simp]
@@ -2018,12 +1956,10 @@ theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNatEmb m i := le_coe_a
 #align fin.sub_nat_add_nat Fin.subNat_addNat
 -/
 
-#print Fin.natAdd_subNat_castIso /-
 @[simp]
-theorem natAdd_subNat_castIso {i : Fin (n + m)} (h : n ≤ i) :
+theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
     natAddEmb n (subNat n (castIso (add_comm _ _) i) h) = i := by simp [← cast_add_nat]
-#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castIso
--/
+#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castₓ
 
 end Pred
 
@@ -2307,7 +2243,7 @@ theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fi
 def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAddEmb n i))
     (hright : ∀ i, C (natAddEmb m i)) (i : Fin (m + n)) : C i :=
   if hi : (i : ℕ) < m then Eq.recOn (castAdd_castLT n i hi) (hleft (castLT i hi))
-  else Eq.recOn (natAdd_subNat_castIso (le_of_not_lt hi)) (hright _)
+  else Eq.recOn (natAdd_subNat_cast (le_of_not_lt hi)) (hright _)
 #align fin.add_cases Fin.addCases
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -457,13 +457,11 @@ theorem val_zero (n : ℕ) [NeZero n] : ((0 : Fin n) : ℕ) = 0 :=
 
 attribute [simp] val_zero
 
-/- warning: fin.val_zero' clashes with fin.coe_zero -> Fin.val_zero
-Case conversion may be inaccurate. Consider using '#align fin.val_zero' Fin.val_zeroₓ'. -/
-#print Fin.val_zero /-
+#print Fin.val_zero' /-
 @[simp]
-theorem val_zero (n) [NeZero n] : (0 : Fin n).val = 0 :=
+theorem val_zero' (n) [NeZero n] : (0 : Fin n).val = 0 :=
   rfl
-#align fin.val_zero' Fin.val_zero
+#align fin.val_zero' Fin.val_zero'
 -/
 
 #print Fin.mk_zero /-
@@ -473,11 +471,11 @@ theorem mk_zero [NeZero n] : (⟨0, Nat.pos_of_ne_zero (NeZero.ne n)⟩ : Fin n)
 #align fin.mk_zero Fin.mk_zero
 -/
 
-#print Fin.zero_le /-
+#print Fin.zero_le' /-
 @[simp]
-theorem zero_le [NeZero n] (a : Fin n) : 0 ≤ a :=
+theorem zero_le' [NeZero n] (a : Fin n) : 0 ≤ a :=
   zero_le a.1
-#align fin.zero_le Fin.zero_le
+#align fin.zero_le Fin.zero_le'
 -/
 
 #print Fin.zero_lt_one /-
@@ -493,10 +491,10 @@ theorem not_lt_zero (a : Fin n.succ) : ¬a < 0 :=
 #align fin.not_lt_zero Fin.not_lt_zero
 -/
 
-#print Fin.pos_iff_ne_zero /-
-theorem pos_iff_ne_zero [NeZero n] (a : Fin n) : 0 < a ↔ a ≠ 0 := by
+#print Fin.pos_iff_ne_zero' /-
+theorem pos_iff_ne_zero' [NeZero n] (a : Fin n) : 0 < a ↔ a ≠ 0 := by
   rw [← coe_fin_lt, coe_zero, pos_iff_ne_zero, Ne.def, Ne.def, ext_iff, coe_zero]
-#align fin.pos_iff_ne_zero Fin.pos_iff_ne_zero
+#align fin.pos_iff_ne_zero Fin.pos_iff_ne_zero'
 -/
 
 #print Fin.eq_zero_or_eq_succ /-
@@ -651,7 +649,7 @@ instance : BoundedOrder (Fin (n + 1)) where
   top := last n
   le_top := le_last
   bot := 0
-  bot_le := zero_le
+  bot_le := zero_le'
 
 instance : Lattice (Fin (n + 1)) :=
   LinearOrder.toLattice
@@ -1127,40 +1125,40 @@ theorem succ_ne_zero {n} : ∀ k : Fin n, Fin.succ k ≠ 0
 #align fin.succ_ne_zero Fin.succ_ne_zero
 -/
 
-#print Fin.succ_zero_eq_one /-
+#print Fin.succ_zero_eq_one' /-
 @[simp]
-theorem succ_zero_eq_one [NeZero n] : Fin.succ (0 : Fin n) = 1 :=
+theorem succ_zero_eq_one' [NeZero n] : Fin.succ (0 : Fin n) = 1 :=
   by
   cases n
   · exact (NeZero.ne 0 rfl).elim
   · rfl
-#align fin.succ_zero_eq_one Fin.succ_zero_eq_one
+#align fin.succ_zero_eq_one Fin.succ_zero_eq_one'
 -/
 
-#print Fin.succ_zero_eq_one' /-
+#print Fin.succ_zero_eq_one /-
 /-- Version of `succ_zero_eq_one` to be used by `dsimp` -/
 @[simp]
-theorem succ_zero_eq_one' : Fin.succ (0 : Fin (n + 1)) = 1 :=
+theorem succ_zero_eq_one : Fin.succ (0 : Fin (n + 1)) = 1 :=
   rfl
-#align fin.succ_zero_eq_one' Fin.succ_zero_eq_one'
+#align fin.succ_zero_eq_one' Fin.succ_zero_eq_one
 -/
 
-#print Fin.succ_one_eq_two /-
+#print Fin.succ_one_eq_two' /-
 @[simp]
-theorem succ_one_eq_two [NeZero n] : Fin.succ (1 : Fin (n + 1)) = 2 :=
+theorem succ_one_eq_two' [NeZero n] : Fin.succ (1 : Fin (n + 1)) = 2 :=
   by
   cases n
   · exact (NeZero.ne 0 rfl).elim
   · rfl
-#align fin.succ_one_eq_two Fin.succ_one_eq_two
+#align fin.succ_one_eq_two Fin.succ_one_eq_two'
 -/
 
-#print Fin.succ_one_eq_two' /-
+#print Fin.succ_one_eq_two /-
 /-- Version of `succ_one_eq_two` to be used by `dsimp` -/
 @[simp]
-theorem succ_one_eq_two' : Fin.succ (1 : Fin (n + 2)) = 2 :=
+theorem succ_one_eq_two : Fin.succ (1 : Fin (n + 2)) = 2 :=
   rfl
-#align fin.succ_one_eq_two' Fin.succ_one_eq_two'
+#align fin.succ_one_eq_two' Fin.succ_one_eq_two
 -/
 
 #print Fin.succ_mk /-
@@ -1226,11 +1224,11 @@ theorem lt_add_one_iff {n : ℕ} {k : Fin (n + 1)} : k < k + 1 ↔ k < last n :=
 #align fin.lt_add_one_iff Fin.lt_add_one_iff
 -/
 
-#print Fin.le_zero_iff /-
+#print Fin.le_zero_iff' /-
 @[simp]
-theorem le_zero_iff {n : ℕ} [NeZero n] {k : Fin n} : k ≤ 0 ↔ k = 0 :=
+theorem le_zero_iff' {n : ℕ} [NeZero n] {k : Fin n} : k ≤ 0 ↔ k = 0 :=
   ⟨fun h => Fin.eq_of_veq <| by rw [Nat.eq_zero_of_le_zero h] <;> rfl, by rintro rfl <;> rfl⟩
-#align fin.le_zero_iff Fin.le_zero_iff
+#align fin.le_zero_iff Fin.le_zero_iff'
 -/
 
 #print Fin.succ_succ_ne_one /-
@@ -1613,11 +1611,11 @@ theorem castSucc_lt_last (a : Fin n) : castSuccEmb a < last n :=
 #align fin.cast_succ_lt_last Fin.castSucc_lt_last
 -/
 
-#print Fin.castSucc_zero /-
+#print Fin.castSucc_zero' /-
 @[simp]
-theorem castSucc_zero [NeZero n] : castSuccEmb (0 : Fin n) = 0 :=
+theorem castSucc_zero' [NeZero n] : castSuccEmb (0 : Fin n) = 0 :=
   rfl
-#align fin.cast_succ_zero Fin.castSucc_zero
+#align fin.cast_succ_zero Fin.castSucc_zero'
 -/
 
 #print Fin.castSucc_one /-
@@ -1627,23 +1625,23 @@ theorem castSucc_one {n : ℕ} : Fin.castSuccEmb (1 : Fin (n + 2)) = 1 :=
 #align fin.cast_succ_one Fin.castSucc_one
 -/
 
-#print Fin.castSucc_pos /-
+#print Fin.castSucc_pos' /-
 /-- `cast_succ i` is positive when `i` is positive -/
-theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSuccEmb i := by
+theorem castSucc_pos' [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSuccEmb i := by
   simpa [lt_iff_coe_lt_coe] using h
-#align fin.cast_succ_pos Fin.castSucc_pos
+#align fin.cast_succ_pos Fin.castSucc_pos'
 -/
 
-#print Fin.castSucc_eq_zero_iff /-
+#print Fin.castSucc_eq_zero_iff' /-
 @[simp]
-theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
+theorem castSucc_eq_zero_iff' [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
   Fin.ext_iff.trans <| (Fin.ext_iff.trans <| Iff.rfl).symm
-#align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iff
+#align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iff'
 -/
 
 #print Fin.castSucc_ne_zero_iff /-
 theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
-  not_iff_not.mpr <| castSucc_eq_zero_iff a
+  not_iff_not.mpr <| castSucc_eq_zero_iff' a
 #align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iff
 -/
 
@@ -2000,7 +1998,7 @@ theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
 #print Fin.pred_castSucc_succ /-
 @[simp]
 theorem pred_castSucc_succ (i : Fin n) :
-    pred (castSuccEmb i.succ) (ne_of_gt (castSucc_pos i.succ_pos)) = i.cast_succ := by
+    pred (castSuccEmb i.succ) (ne_of_gt (castSucc_pos' i.succ_pos)) = i.cast_succ := by
   simp [eq_iff_veq]
 #align fin.pred_cast_succ_succ Fin.pred_castSucc_succ
 -/
@@ -2253,25 +2251,25 @@ termination_by' ⟨_, measure_wf fun i : Fin (n + 1) => n + 1 - i⟩
 #align fin.reverse_induction Fin.reverseInduction
 -/
 
-#print Fin.reverse_induction_last /-
+#print Fin.reverseInduction_last /-
 @[simp]
-theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
+theorem reverseInduction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) :
     (reverseInduction h0 hs (Fin.last n) : C (Fin.last n)) = h0 := by
   rw [reverse_induction] <;> simp
-#align fin.reverse_induction_last Fin.reverse_induction_last
+#align fin.reverse_induction_last Fin.reverseInduction_last
 -/
 
-#print Fin.reverse_induction_castSucc /-
+#print Fin.reverseInduction_castSucc /-
 @[simp]
-theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
+theorem reverseInduction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) (i : Fin n) :
     (reverseInduction h0 hs i.cast_succ : C i.cast_succ) = hs i (reverseInduction h0 hs i.succ) :=
   by
   rw [reverse_induction, dif_neg (ne_of_lt (Fin.castSucc_lt_last i))]
   cases i
   rfl
-#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSucc
+#align fin.reverse_induction_cast_succ Fin.reverseInduction_castSucc
 -/
 
 #print Fin.lastCases /-
@@ -2289,7 +2287,7 @@ def lastCases {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
 theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) :
     (Fin.lastCases hlast hcast (Fin.last n) : C (Fin.last n)) = hlast :=
-  reverse_induction_last _ _
+  reverseInduction_last _ _
 #align fin.last_cases_last Fin.lastCases_last
 -/
 
@@ -2298,7 +2296,7 @@ theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.la
 theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) (i : Fin n) :
     (Fin.lastCases hlast hcast (Fin.castSuccEmb i) : C (Fin.castSuccEmb i)) = hcast i :=
-  reverse_induction_castSucc _ _ _
+  reverseInduction_castSucc _ _ _
 #align fin.last_cases_cast_succ Fin.lastCases_castSucc
 -/
 
@@ -2861,7 +2859,7 @@ section PredAbove
 #print Fin.predAbove /-
 /-- `pred_above p i` embeds `i : fin (n+1)` into `fin n` by subtracting one if `p < i`. -/
 def predAbove (p : Fin n) (i : Fin (n + 1)) : Fin n :=
-  if h : p.cast_succ < i then i.pred (ne_of_lt (lt_of_le_of_lt (zero_le p.cast_succ) h)).symm
+  if h : p.cast_succ < i then i.pred (ne_of_lt (lt_of_le_of_lt (zero_le' p.cast_succ) h)).symm
   else i.castLT (lt_of_le_of_lt (le_of_not_lt h) p.2)
 #align fin.pred_above Fin.predAbove
 -/
@@ -3177,16 +3175,16 @@ theorem coe_mul {n : ℕ} : ∀ a b : Fin n, ((a * b : Fin n) : ℕ) = a * b % n
 #align fin.coe_mul Fin.coe_mul
 -/
 
-#print Fin.mul_one /-
+#print Fin.mul_one' /-
 @[simp]
-protected theorem mul_one [NeZero n] (k : Fin n) : k * 1 = k :=
+protected theorem mul_one' [NeZero n] (k : Fin n) : k * 1 = k :=
   by
   cases n
   · simp
   cases n
   · simp
   simp [eq_iff_veq, mul_def, mod_eq_of_lt (is_lt k)]
-#align fin.mul_one Fin.mul_one
+#align fin.mul_one Fin.mul_one'
 -/
 
 #print Fin.mul_comm /-
@@ -3195,24 +3193,24 @@ protected theorem mul_comm (a b : Fin n) : a * b = b * a :=
 #align fin.mul_comm Fin.mul_comm
 -/
 
-#print Fin.one_mul /-
+#print Fin.one_mul' /-
 @[simp]
-protected theorem one_mul [NeZero n] (k : Fin n) : (1 : Fin n) * k = k := by
-  rw [Fin.mul_comm, Fin.mul_one]
-#align fin.one_mul Fin.one_mul
+protected theorem one_mul' [NeZero n] (k : Fin n) : (1 : Fin n) * k = k := by
+  rw [Fin.mul_comm, Fin.mul_one']
+#align fin.one_mul Fin.one_mul'
 -/
 
-#print Fin.mul_zero /-
+#print Fin.mul_zero' /-
 @[simp]
-protected theorem mul_zero [NeZero n] (k : Fin n) : k * 0 = 0 := by simp [eq_iff_veq, mul_def]
-#align fin.mul_zero Fin.mul_zero
+protected theorem mul_zero' [NeZero n] (k : Fin n) : k * 0 = 0 := by simp [eq_iff_veq, mul_def]
+#align fin.mul_zero Fin.mul_zero'
 -/
 
-#print Fin.zero_mul /-
+#print Fin.zero_mul' /-
 @[simp]
-protected theorem zero_mul [NeZero n] (k : Fin n) : (0 : Fin n) * k = 0 := by
+protected theorem zero_mul' [NeZero n] (k : Fin n) : (0 : Fin n) * k = 0 := by
   simp [eq_iff_veq, mul_def]
-#align fin.zero_mul Fin.zero_mul
+#align fin.zero_mul Fin.zero_mul'
 -/
 
 end Mul

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Keeley Hoek
-
-! This file was ported from Lean 3 source module data.fin.basic
-! leanprover-community/mathlib commit 3a2b5524a138b5d0b818b858b516d4ac8a484b03
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.NeZero
 import Mathbin.Algebra.Order.WithZero
@@ -14,6 +9,8 @@ import Mathbin.Order.RelIso.Basic
 import Mathbin.Data.Nat.Order.Basic
 import Mathbin.Order.Hom.Set
 
+#align_import data.fin.basic from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"
+
 /-!
 # The finite type with `n` elements
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -807,12 +807,14 @@ theorem subsingleton_iff_le_one : Subsingleton (Fin n) ↔ n ≤ 1 := by
 
 section Monoid
 
+#print Fin.addCommSemigroup /-
 instance addCommSemigroup (n : ℕ) : AddCommSemigroup (Fin n)
     where
   add := (· + ·)
   add_assoc := by simp [eq_iff_veq, add_def, add_assoc]
   add_comm := by simp [eq_iff_veq, add_def, add_comm]
 #align fin.add_comm_semigroup Fin.addCommSemigroup
+-/
 
 #print Fin.add_zero /-
 @[simp]
@@ -2426,11 +2428,11 @@ instance (n : ℕ) : IsCancelAdd (Fin n)
 
 /-- Note this is more general than `fin.add_comm_group` as it applies (vacuously) to `fin 0` too. -/
 instance (n : ℕ) : AddLeftCancelSemigroup (Fin n) :=
-  { Fin.addCommSemigroup n, Fin.isCancelAdd n with }
+  { Fin.addCommSemigroup n, Fin.instIsCancelAdd n with }
 
 /-- Note this is more general than `fin.add_comm_group` as it applies (vacuously) to `fin 0` too. -/
 instance (n : ℕ) : AddRightCancelSemigroup (Fin n) :=
-  { Fin.addCommSemigroup n, Fin.isCancelAdd n with }
+  { Fin.addCommSemigroup n, Fin.instIsCancelAdd n with }
 
 #print Fin.coe_neg /-
 protected theorem coe_neg (a : Fin n) : ((-a : Fin n) : ℕ) = (n - a) % n :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

@@ -1261,16 +1261,16 @@ theorem castLT_mk (i n m : ℕ) (hn : i < n) (hm : i < m) : castLT ⟨i, hn⟩ h
 #align fin.cast_lt_mk Fin.castLT_mk
 -/
 
-#print Fin.castLE /-
+#print Fin.castLEEmb /-
 /-- `cast_le h i` embeds `i` into a larger `fin` type.  -/
-def castLE (h : n ≤ m) : Fin n ↪o Fin m :=
+def castLEEmb (h : n ≤ m) : Fin n ↪o Fin m :=
   OrderEmbedding.ofStrictMono (fun a => castLT a (lt_of_lt_of_le a.2 h)) fun a b h => h
-#align fin.cast_le Fin.castLE
+#align fin.cast_le Fin.castLEEmb
 -/
 
 #print Fin.coe_castLE /-
 @[simp]
-theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
+theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLEEmb h i : ℕ) = i :=
   rfl
 #align fin.coe_cast_le Fin.coe_castLE
 -/
@@ -1278,45 +1278,45 @@ theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
 #print Fin.castLE_mk /-
 @[simp]
 theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
-    castLE h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h⟩ :=
+    castLEEmb h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h⟩ :=
   rfl
 #align fin.cast_le_mk Fin.castLE_mk
 -/
 
 #print Fin.castLE_zero /-
 @[simp]
-theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [eq_iff_veq]
+theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLEEmb h 0 = 0 := by simp [eq_iff_veq]
 #align fin.cast_le_zero Fin.castLE_zero
 -/
 
 #print Fin.range_castLE /-
 @[simp]
-theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = {i | (i : ℕ) < n} :=
+theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLEEmb h) = {i | (i : ℕ) < n} :=
   Set.ext fun x => ⟨fun ⟨y, hy⟩ => hy ▸ y.2, fun hx => ⟨⟨x, hx⟩, Fin.ext rfl⟩⟩
 #align fin.range_cast_le Fin.range_castLE
 -/
 
-#print Fin.coe_of_injective_castLE_symm /-
+#print Fin.coe_of_injective_castLEEmb_symm /-
 @[simp]
-theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
-    ((Equiv.ofInjective _ (castLE h).Injective).symm ⟨i, hi⟩ : ℕ) = i :=
+theorem coe_of_injective_castLEEmb_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
+    ((Equiv.ofInjective _ (castLEEmb h).Injective).symm ⟨i, hi⟩ : ℕ) = i :=
   by
   rw [← coe_cast_le]
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
-#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symm
+#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLEEmb_symm
 -/
 
 #print Fin.castLE_succ /-
 @[simp]
 theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
-    castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.eq_iff_veq]
+    castLEEmb h i.succ = (castLEEmb (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.eq_iff_veq]
 #align fin.cast_le_succ Fin.castLE_succ
 -/
 
 #print Fin.castLE_castLE /-
 @[simp]
 theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
-    Fin.castLE mn (Fin.castLE km i) = Fin.castLE (km.trans mn) i :=
+    Fin.castLEEmb mn (Fin.castLEEmb km i) = Fin.castLEEmb (km.trans mn) i :=
   Fin.ext (by simp only [coe_cast_le])
 #align fin.cast_le_cast_le Fin.castLE_castLE
 -/
@@ -1324,7 +1324,7 @@ theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
 #print Fin.castLE_comp_castLE /-
 @[simp]
 theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
-    Fin.castLE mn ∘ Fin.castLE km = Fin.castLE (km.trans mn) :=
+    Fin.castLEEmb mn ∘ Fin.castLEEmb km = Fin.castLEEmb (km.trans mn) :=
   funext (castLE_castLE km mn)
 #align fin.cast_le_comp_cast_le Fin.castLE_comp_castLE
 -/
@@ -1333,7 +1333,7 @@ theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
 /-- `cast eq i` embeds `i` into a equal `fin` type, see also `equiv.fin_congr`. -/
 def castIso (eq : n = m) : Fin n ≃o Fin m
     where
-  toEquiv := ⟨castLE Eq.le, castLE Eq.symm.le, fun a => eq_of_veq rfl, fun a => eq_of_veq rfl⟩
+  toEquiv := ⟨castLEEmb Eq.le, castLEEmb Eq.symm.le, fun a => eq_of_veq rfl, fun a => eq_of_veq rfl⟩
   map_rel_iff' a b := Iff.rfl
 #align fin.cast Fin.castIso
 -/
@@ -1395,7 +1395,7 @@ theorem castIso_refl (h : n = n := rfl) : castIso h = OrderIso.refl (Fin n) := b
 
 #print Fin.castLE_of_eq /-
 theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
-    (castLE h' : Fin m → Fin n) = Fin.castIso h :=
+    (castLEEmb h' : Fin m → Fin n) = Fin.castIso h :=
   funext fun _ => rfl
 #align fin.cast_le_of_eq Fin.castLE_of_eq
 -/
@@ -1416,50 +1416,51 @@ theorem castIso_eq_cast (h : n = m) : (castIso h : Fin n → Fin m) = cast (h 
 #align fin.cast_eq_cast Fin.castIso_eq_cast
 -/
 
-#print Fin.castAdd /-
+#print Fin.castAddEmb /-
 /-- `cast_add m i` embeds `i : fin n` in `fin (n+m)`. See also `fin.nat_add` and `fin.add_nat`. -/
-def castAdd (m) : Fin n ↪o Fin (n + m) :=
-  castLE <| Nat.le_add_right n m
-#align fin.cast_add Fin.castAdd
+def castAddEmb (m) : Fin n ↪o Fin (n + m) :=
+  castLEEmb <| Nat.le_add_right n m
+#align fin.cast_add Fin.castAddEmb
 -/
 
 #print Fin.coe_castAdd /-
 @[simp]
-theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
+theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAddEmb m i : ℕ) = i :=
   rfl
 #align fin.coe_cast_add Fin.coe_castAdd
 -/
 
 #print Fin.castAdd_zero /-
 @[simp]
-theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = castIso rfl :=
+theorem castAdd_zero : (castAddEmb 0 : Fin n → Fin (n + 0)) = castIso rfl :=
   rfl
 #align fin.cast_add_zero Fin.castAdd_zero
 -/
 
 #print Fin.castAdd_lt /-
-theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAdd n i : ℕ) < m :=
+theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAddEmb n i : ℕ) < m :=
   i.2
 #align fin.cast_add_lt Fin.castAdd_lt
 -/
 
 #print Fin.castAdd_mk /-
 @[simp]
-theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i, lt_add_right i n m h⟩ :=
+theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAddEmb m ⟨i, h⟩ = ⟨i, lt_add_right i n m h⟩ :=
   rfl
 #align fin.cast_add_mk Fin.castAdd_mk
 -/
 
 #print Fin.castAdd_castLT /-
 @[simp]
-theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m (castLT i hi) = i :=
+theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) :
+    castAddEmb m (castLT i hi) = i :=
   ext rfl
 #align fin.cast_add_cast_lt Fin.castAdd_castLT
 -/
 
 #print Fin.castLT_castAdd /-
 @[simp]
-theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt m i) = i :=
+theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAddEmb m i) (castAdd_lt m i) = i :=
   ext rfl
 #align fin.cast_lt_cast_add Fin.castLT_castAdd
 -/
@@ -1467,14 +1468,14 @@ theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt
 #print Fin.castAdd_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_castIso {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
-    castAdd m (Fin.castIso h i) = Fin.castIso (congr_arg _ h) (castAdd m i) :=
+    castAddEmb m (Fin.castIso h i) = Fin.castIso (congr_arg _ h) (castAddEmb m i) :=
   ext rfl
 #align fin.cast_add_cast Fin.castAdd_castIso
 -/
 
 #print Fin.castIso_castAdd_left /-
 theorem castIso_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
-    castIso h (castAdd m i) = castAdd m (castIso (add_right_cancel h) i) :=
+    castIso h (castAddEmb m i) = castAddEmb m (castIso (add_right_cancel h) i) :=
   ext rfl
 #align fin.cast_cast_add_left Fin.castIso_castAdd_left
 -/
@@ -1482,14 +1483,14 @@ theorem castIso_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 #print Fin.castIso_castAdd_right /-
 @[simp]
 theorem castIso_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
-    castIso h (castAdd m' i) = castAdd m i :=
+    castIso h (castAddEmb m' i) = castAddEmb m i :=
   ext rfl
 #align fin.cast_cast_add_right Fin.castIso_castAdd_right
 -/
 
 #print Fin.castAdd_castAdd /-
 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
-    castAdd p (castAdd n i) = castIso (add_assoc _ _ _).symm (castAdd (n + p) i) :=
+    castAddEmb p (castAddEmb n i) = castIso (add_assoc _ _ _).symm (castAddEmb (n + p) i) :=
   ext rfl
 #align fin.cast_add_cast_add Fin.castAdd_castAdd
 -/
@@ -1514,50 +1515,50 @@ theorem succ_castIso_eq {n' : ℕ} (i : Fin n) (h : n = n') :
 #print Fin.castSuccEmb /-
 /-- `cast_succ i` embeds `i : fin n` in `fin (n+1)`. -/
 def castSuccEmb : Fin n ↪o Fin (n + 1) :=
-  castAdd 1
+  castAddEmb 1
 #align fin.cast_succ Fin.castSuccEmb
 -/
 
-#print Fin.coe_castSuccEmb /-
+#print Fin.coe_castSucc /-
 @[simp]
-theorem coe_castSuccEmb (i : Fin n) : (i.cast_succ : ℕ) = i :=
+theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
   rfl
-#align fin.coe_cast_succ Fin.coe_castSuccEmb
+#align fin.coe_cast_succ Fin.coe_castSucc
 -/
 
-#print Fin.castSuccEmb_mk /-
+#print Fin.castSucc_mk /-
 @[simp]
-theorem castSuccEmb_mk (n i : ℕ) (h : i < n) : castSuccEmb ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
+theorem castSucc_mk (n i : ℕ) (h : i < n) : castSuccEmb ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
   rfl
-#align fin.cast_succ_mk Fin.castSuccEmb_mk
+#align fin.cast_succ_mk Fin.castSucc_mk
 -/
 
-#print Fin.castIso_castSuccEmb /-
+#print Fin.castIso_castSucc /-
 @[simp]
-theorem castIso_castSuccEmb {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
+theorem castIso_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
     castIso h (castSuccEmb i) = castSuccEmb (castIso (Nat.succ_injective h) i) := by ext;
   simp only [coe_cast, coe_cast_succ]
-#align fin.cast_cast_succ Fin.castIso_castSuccEmb
+#align fin.cast_cast_succ Fin.castIso_castSucc
 -/
 
-#print Fin.castSuccEmb_lt_succ /-
-theorem castSuccEmb_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
+#print Fin.castSucc_lt_succ /-
+theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
   lt_iff_val_lt_val.2 <| by simp only [coe_cast_succ, coe_succ, Nat.lt_succ_self]
-#align fin.cast_succ_lt_succ Fin.castSuccEmb_lt_succ
+#align fin.cast_succ_lt_succ Fin.castSucc_lt_succ
 -/
 
-#print Fin.le_castSuccEmb_iff /-
-theorem le_castSuccEmb_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
+#print Fin.le_castSucc_iff /-
+theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
   simpa [lt_iff_coe_lt_coe, le_iff_coe_le_coe] using nat.succ_le_succ_iff.symm
-#align fin.le_cast_succ_iff Fin.le_castSuccEmb_iff
+#align fin.le_cast_succ_iff Fin.le_castSucc_iff
 -/
 
-#print Fin.castSuccEmb_lt_iff_succ_le /-
-theorem castSuccEmb_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
+#print Fin.castSucc_lt_iff_succ_le /-
+theorem castSucc_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
     i.cast_succ < j ↔ i.succ ≤ j := by
-  simpa only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSuccEmb] using
+  simpa only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc] using
     Nat.lt_iff_add_one_le
-#align fin.cast_succ_lt_iff_succ_le Fin.castSuccEmb_lt_iff_succ_le
+#align fin.cast_succ_lt_iff_succ_le Fin.castSucc_lt_iff_succ_le
 -/
 
 #print Fin.succ_last /-
@@ -1574,92 +1575,92 @@ theorem succ_eq_last_succ {n : ℕ} (i : Fin n.succ) : i.succ = last (n + 1) ↔
 #align fin.succ_eq_last_succ Fin.succ_eq_last_succ
 -/
 
-#print Fin.castSuccEmb_castLT /-
+#print Fin.castSucc_castLT /-
 @[simp]
-theorem castSuccEmb_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSuccEmb (castLT i h) = i :=
+theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSuccEmb (castLT i h) = i :=
   Fin.eq_of_veq rfl
-#align fin.cast_succ_cast_lt Fin.castSuccEmb_castLT
+#align fin.cast_succ_cast_lt Fin.castSucc_castLT
 -/
 
-#print Fin.castLT_castSuccEmb /-
+#print Fin.castLT_castSucc /-
 @[simp]
-theorem castLT_castSuccEmb {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSuccEmb a) h = a :=
-  by cases a <;> rfl
-#align fin.cast_lt_cast_succ Fin.castLT_castSuccEmb
+theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSuccEmb a) h = a := by
+  cases a <;> rfl
+#align fin.cast_lt_cast_succ Fin.castLT_castSucc
 -/
 
-#print Fin.castSuccEmb_lt_castSuccEmb_iff /-
+#print Fin.castSucc_lt_castSucc_iff /-
 @[simp]
-theorem castSuccEmb_lt_castSuccEmb_iff : a.cast_succ < b.cast_succ ↔ a < b :=
+theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
   (@castSuccEmb n).lt_iff_lt
-#align fin.cast_succ_lt_cast_succ_iff Fin.castSuccEmb_lt_castSuccEmb_iff
+#align fin.cast_succ_lt_cast_succ_iff Fin.castSucc_lt_castSucc_iff
 -/
 
-#print Fin.castSuccEmb_injective /-
-theorem castSuccEmb_injective (n : ℕ) : Injective (@Fin.castSuccEmb n) :=
+#print Fin.castSucc_injective /-
+theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSuccEmb n) :=
   (castSuccEmb : Fin n ↪o _).Injective
-#align fin.cast_succ_injective Fin.castSuccEmb_injective
+#align fin.cast_succ_injective Fin.castSucc_injective
 -/
 
-#print Fin.castSuccEmb_inj /-
-theorem castSuccEmb_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
-  (castSuccEmb_injective n).eq_iff
-#align fin.cast_succ_inj Fin.castSuccEmb_inj
+#print Fin.castSucc_inj /-
+theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
+  (castSucc_injective n).eq_iff
+#align fin.cast_succ_inj Fin.castSucc_inj
 -/
 
-#print Fin.castSuccEmb_lt_last /-
-theorem castSuccEmb_lt_last (a : Fin n) : castSuccEmb a < last n :=
+#print Fin.castSucc_lt_last /-
+theorem castSucc_lt_last (a : Fin n) : castSuccEmb a < last n :=
   lt_iff_val_lt_val.mpr a.is_lt
-#align fin.cast_succ_lt_last Fin.castSuccEmb_lt_last
+#align fin.cast_succ_lt_last Fin.castSucc_lt_last
 -/
 
-#print Fin.castSuccEmb_zero /-
+#print Fin.castSucc_zero /-
 @[simp]
-theorem castSuccEmb_zero [NeZero n] : castSuccEmb (0 : Fin n) = 0 :=
+theorem castSucc_zero [NeZero n] : castSuccEmb (0 : Fin n) = 0 :=
   rfl
-#align fin.cast_succ_zero Fin.castSuccEmb_zero
+#align fin.cast_succ_zero Fin.castSucc_zero
 -/
 
-#print Fin.castSuccEmb_one /-
+#print Fin.castSucc_one /-
 @[simp]
-theorem castSuccEmb_one {n : ℕ} : Fin.castSuccEmb (1 : Fin (n + 2)) = 1 :=
+theorem castSucc_one {n : ℕ} : Fin.castSuccEmb (1 : Fin (n + 2)) = 1 :=
   rfl
-#align fin.cast_succ_one Fin.castSuccEmb_one
+#align fin.cast_succ_one Fin.castSucc_one
 -/
 
-#print Fin.castSuccEmb_pos /-
+#print Fin.castSucc_pos /-
 /-- `cast_succ i` is positive when `i` is positive -/
-theorem castSuccEmb_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSuccEmb i := by
+theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSuccEmb i := by
   simpa [lt_iff_coe_lt_coe] using h
-#align fin.cast_succ_pos Fin.castSuccEmb_pos
+#align fin.cast_succ_pos Fin.castSucc_pos
 -/
 
-#print Fin.castSuccEmb_eq_zero_iff /-
+#print Fin.castSucc_eq_zero_iff /-
 @[simp]
-theorem castSuccEmb_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
+theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
   Fin.ext_iff.trans <| (Fin.ext_iff.trans <| Iff.rfl).symm
-#align fin.cast_succ_eq_zero_iff Fin.castSuccEmb_eq_zero_iff
+#align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iff
 -/
 
-#print Fin.castSuccEmb_ne_zero_iff /-
-theorem castSuccEmb_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
-  not_iff_not.mpr <| castSuccEmb_eq_zero_iff a
-#align fin.cast_succ_ne_zero_iff Fin.castSuccEmb_ne_zero_iff
+#print Fin.castSucc_ne_zero_iff /-
+theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
+  not_iff_not.mpr <| castSucc_eq_zero_iff a
+#align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iff
 -/
 
-#print Fin.castSuccEmb_fin_succ /-
-theorem castSuccEmb_fin_succ (n : ℕ) (j : Fin n) :
+#print Fin.castSucc_fin_succ /-
+theorem castSucc_fin_succ (n : ℕ) (j : Fin n) :
     castSuccEmb (Fin.succ j) = Fin.succ (castSuccEmb j) := by simp [Fin.ext_iff]
-#align fin.cast_succ_fin_succ Fin.castSuccEmb_fin_succ
+#align fin.cast_succ_fin_succ Fin.castSucc_fin_succ
 -/
 
-#print Fin.coe_eq_castSuccEmb /-
+#print Fin.coe_eq_castSucc /-
 @[norm_cast, simp]
-theorem coe_eq_castSuccEmb : (a : Fin (n + 1)) = a.cast_succ :=
+theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
   by
   ext
   exact coe_val_of_lt (Nat.lt.step a.is_lt)
-#align fin.coe_eq_cast_succ Fin.coe_eq_castSuccEmb
+#align fin.coe_eq_cast_succ Fin.coe_eq_castSucc
 -/
 
 #print Fin.coeSucc_eq_succ /-
@@ -1678,60 +1679,59 @@ theorem lt_succ : a.cast_succ < a.succ := by
 #align fin.lt_succ Fin.lt_succ
 -/
 
-#print Fin.range_castSuccEmb /-
+#print Fin.range_castSucc /-
 @[simp]
-theorem range_castSuccEmb {n : ℕ} :
-    Set.range (castSuccEmb : Fin n → Fin n.succ) = {i | (i : ℕ) < n} :=
+theorem range_castSucc {n : ℕ} : Set.range (castSuccEmb : Fin n → Fin n.succ) = {i | (i : ℕ) < n} :=
   range_castLE _
-#align fin.range_cast_succ Fin.range_castSuccEmb
+#align fin.range_cast_succ Fin.range_castSucc
 -/
 
-#print Fin.coe_of_injective_castSuccEmb_symm /-
+#print Fin.coe_of_injective_castSucc_symm /-
 @[simp]
-theorem coe_of_injective_castSuccEmb_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
-    ((Equiv.ofInjective castSuccEmb (castSuccEmb_injective _)).symm ⟨i, hi⟩ : ℕ) = i :=
+theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
+    ((Equiv.ofInjective castSuccEmb (castSucc_injective _)).symm ⟨i, hi⟩ : ℕ) = i :=
   by
   rw [← coe_cast_succ]
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
-#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSuccEmb_symm
+#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symm
 -/
 
-#print Fin.succ_castSuccEmb /-
-theorem succ_castSuccEmb {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
+#print Fin.succ_castSucc /-
+theorem succ_castSucc {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
   Fin.ext (by simp)
-#align fin.succ_cast_succ Fin.succ_castSuccEmb
+#align fin.succ_cast_succ Fin.succ_castSucc
 -/
 
-#print Fin.addNat /-
+#print Fin.addNatEmb /-
 /-- `add_nat m i` adds `m` to `i`, generalizes `fin.succ`. -/
-def addNat (m) : Fin n ↪o Fin (n + m) :=
+def addNatEmb (m) : Fin n ↪o Fin (n + m) :=
   OrderEmbedding.ofStrictMono (fun i => ⟨(i : ℕ) + m, add_lt_add_right i.2 _⟩) fun i j h =>
     lt_iff_val_lt_val.2 <| add_lt_add_right h _
-#align fin.add_nat Fin.addNat
+#align fin.add_nat Fin.addNatEmb
 -/
 
 #print Fin.coe_addNat /-
 @[simp]
-theorem coe_addNat (m : ℕ) (i : Fin n) : (addNat m i : ℕ) = i + m :=
+theorem coe_addNat (m : ℕ) (i : Fin n) : (addNatEmb m i : ℕ) = i + m :=
   rfl
 #align fin.coe_add_nat Fin.coe_addNat
 -/
 
 #print Fin.addNat_one /-
 @[simp]
-theorem addNat_one {i : Fin n} : addNat 1 i = i.succ := by ext; rw [coe_add_nat, coe_succ]
+theorem addNat_one {i : Fin n} : addNatEmb 1 i = i.succ := by ext; rw [coe_add_nat, coe_succ]
 #align fin.add_nat_one Fin.addNat_one
 -/
 
 #print Fin.le_coe_addNat /-
-theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNat m i :=
+theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNatEmb m i :=
   Nat.le_add_left _ _
 #align fin.le_coe_add_nat Fin.le_coe_addNat
 -/
 
 #print Fin.addNat_mk /-
 @[simp]
-theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, add_lt_add_right hi n⟩ :=
+theorem addNat_mk (n i : ℕ) (hi : i < m) : addNatEmb n ⟨i, hi⟩ = ⟨i + n, add_lt_add_right hi n⟩ :=
   rfl
 #align fin.add_nat_mk Fin.addNat_mk
 -/
@@ -1739,7 +1739,7 @@ theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, ad
 #print Fin.castIso_addNat_zero /-
 @[simp]
 theorem castIso_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
-    castIso h (addNat 0 i) = castIso ((add_zero _).symm.trans h) i :=
+    castIso h (addNatEmb 0 i) = castIso ((add_zero _).symm.trans h) i :=
   ext <| add_zero _
 #align fin.cast_add_nat_zero Fin.castIso_addNat_zero
 -/
@@ -1747,14 +1747,14 @@ theorem castIso_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 #print Fin.addNat_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_castIso {n n' m : ℕ} (i : Fin n') (h : n' = n) :
-    addNat m (castIso h i) = castIso (congr_arg _ h) (addNat m i) :=
+    addNatEmb m (castIso h i) = castIso (congr_arg _ h) (addNatEmb m i) :=
   ext rfl
 #align fin.add_nat_cast Fin.addNat_castIso
 -/
 
 #print Fin.castIso_addNat_left /-
 theorem castIso_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
-    castIso h (addNat m i) = addNat m (castIso (add_right_cancel h) i) :=
+    castIso h (addNatEmb m i) = addNatEmb m (castIso (add_right_cancel h) i) :=
   ext rfl
 #align fin.cast_add_nat_left Fin.castIso_addNat_left
 -/
@@ -1762,41 +1762,41 @@ theorem castIso_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 #print Fin.castIso_addNat_right /-
 @[simp]
 theorem castIso_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
-    castIso h (addNat m' i) = addNat m i :=
+    castIso h (addNatEmb m' i) = addNatEmb m i :=
   ext <| (congr_arg ((· + ·) (i : ℕ)) (add_left_cancel h) : _)
 #align fin.cast_add_nat_right Fin.castIso_addNat_right
 -/
 
-#print Fin.natAdd /-
+#print Fin.natAddEmb /-
 /-- `nat_add n i` adds `n` to `i` "on the left". -/
-def natAdd (n) {m} : Fin m ↪o Fin (n + m) :=
+def natAddEmb (n) {m} : Fin m ↪o Fin (n + m) :=
   OrderEmbedding.ofStrictMono (fun i => ⟨n + (i : ℕ), add_lt_add_left i.2 _⟩) fun i j h =>
     lt_iff_val_lt_val.2 <| add_lt_add_left h _
-#align fin.nat_add Fin.natAdd
+#align fin.nat_add Fin.natAddEmb
 -/
 
 #print Fin.coe_natAdd /-
 @[simp]
-theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAdd n i : ℕ) = n + i :=
+theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAddEmb n i : ℕ) = n + i :=
   rfl
 #align fin.coe_nat_add Fin.coe_natAdd
 -/
 
 #print Fin.natAdd_mk /-
 @[simp]
-theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAdd n ⟨i, hi⟩ = ⟨n + i, add_lt_add_left hi n⟩ :=
+theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAddEmb n ⟨i, hi⟩ = ⟨n + i, add_lt_add_left hi n⟩ :=
   rfl
 #align fin.nat_add_mk Fin.natAdd_mk
 -/
 
 #print Fin.le_coe_natAdd /-
-theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAdd m i :=
+theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAddEmb m i :=
   Nat.le_add_right _ _
 #align fin.le_coe_nat_add Fin.le_coe_natAdd
 -/
 
 #print Fin.natAdd_zero /-
-theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.castIso (zero_add n).symm).toRelEmbedding := by
+theorem natAdd_zero {n : ℕ} : Fin.natAddEmb 0 = (Fin.castIso (zero_add n).symm).toRelEmbedding := by
   ext; apply zero_add
 #align fin.nat_add_zero Fin.natAdd_zero
 -/
@@ -1804,14 +1804,14 @@ theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.castIso (zero_add n).symm).t
 #print Fin.natAdd_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
 theorem natAdd_castIso {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
-    natAdd m (castIso h i) = castIso (congr_arg _ h) (natAdd m i) :=
+    natAddEmb m (castIso h i) = castIso (congr_arg _ h) (natAddEmb m i) :=
   ext rfl
 #align fin.nat_add_cast Fin.natAdd_castIso
 -/
 
 #print Fin.castIso_natAdd_right /-
 theorem castIso_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
-    castIso h (natAdd m i) = natAdd m (castIso (add_left_cancel h) i) :=
+    castIso h (natAddEmb m i) = natAddEmb m (castIso (add_left_cancel h) i) :=
   ext rfl
 #align fin.cast_nat_add_right Fin.castIso_natAdd_right
 -/
@@ -1819,28 +1819,28 @@ theorem castIso_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
 #print Fin.castIso_natAdd_left /-
 @[simp]
 theorem castIso_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
-    castIso h (natAdd m' i) = natAdd m i :=
+    castIso h (natAddEmb m' i) = natAddEmb m i :=
   ext <| (congr_arg (· + (i : ℕ)) (add_right_cancel h) : _)
 #align fin.cast_nat_add_left Fin.castIso_natAdd_left
 -/
 
 #print Fin.castAdd_natAdd /-
 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
-    castAdd p (natAdd m i) = castIso (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
+    castAddEmb p (natAddEmb m i) = castIso (add_assoc _ _ _).symm (natAddEmb m (castAddEmb p i)) :=
   ext rfl
 #align fin.cast_add_nat_add Fin.castAdd_natAdd
 -/
 
 #print Fin.natAdd_castAdd /-
 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
-    natAdd m (castAdd p i) = castIso (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
+    natAddEmb m (castAddEmb p i) = castIso (add_assoc _ _ _) (castAddEmb p (natAddEmb m i)) :=
   ext rfl
 #align fin.nat_add_cast_add Fin.natAdd_castAdd
 -/
 
 #print Fin.natAdd_natAdd /-
 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
-    natAdd m (natAdd n i) = castIso (add_assoc _ _ _) (natAdd (m + n) i) :=
+    natAddEmb m (natAddEmb n i) = castIso (add_assoc _ _ _) (natAddEmb (m + n) i) :=
   ext <| (add_assoc _ _ _).symm
 #align fin.nat_add_nat_add Fin.natAdd_natAdd
 -/
@@ -1848,7 +1848,7 @@ theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
 #print Fin.castIso_natAdd_zero /-
 @[simp]
 theorem castIso_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
-    castIso h (natAdd 0 i) = castIso ((zero_add _).symm.trans h) i :=
+    castIso h (natAddEmb 0 i) = castIso ((zero_add _).symm.trans h) i :=
   ext <| zero_add _
 #align fin.cast_nat_add_zero Fin.castIso_natAdd_zero
 -/
@@ -1856,7 +1856,7 @@ theorem castIso_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
 #print Fin.castIso_natAdd /-
 @[simp]
 theorem castIso_natAdd (n : ℕ) {m : ℕ} (i : Fin m) :
-    castIso (add_comm _ _) (natAdd n i) = addNat n i :=
+    castIso (add_comm _ _) (natAddEmb n i) = addNatEmb n i :=
   ext <| add_comm _ _
 #align fin.cast_nat_add Fin.castIso_natAdd
 -/
@@ -1864,23 +1864,23 @@ theorem castIso_natAdd (n : ℕ) {m : ℕ} (i : Fin m) :
 #print Fin.castIso_addNat /-
 @[simp]
 theorem castIso_addNat {n : ℕ} (m : ℕ) (i : Fin n) :
-    castIso (add_comm _ _) (addNat m i) = natAdd m i :=
+    castIso (add_comm _ _) (addNatEmb m i) = natAddEmb m i :=
   ext <| add_comm _ _
 #align fin.cast_add_nat Fin.castIso_addNat
 -/
 
 #print Fin.natAdd_last /-
 @[simp]
-theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
+theorem natAdd_last {m n : ℕ} : natAddEmb n (last m) = last (n + m) :=
   rfl
 #align fin.nat_add_last Fin.natAdd_last
 -/
 
-#print Fin.natAdd_castSuccEmb /-
-theorem natAdd_castSuccEmb {m n : ℕ} {i : Fin m} :
-    natAdd n (castSuccEmb i) = castSuccEmb (natAdd n i) :=
+#print Fin.natAdd_castSucc /-
+theorem natAdd_castSucc {m n : ℕ} {i : Fin m} :
+    natAddEmb n (castSuccEmb i) = castSuccEmb (natAddEmb n i) :=
   rfl
-#align fin.nat_add_cast_succ Fin.natAdd_castSuccEmb
+#align fin.nat_add_cast_succ Fin.natAdd_castSucc
 -/
 
 end Succ
@@ -1998,25 +1998,25 @@ theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
 #align fin.sub_nat_mk Fin.subNat_mk
 -/
 
-#print Fin.pred_castSuccEmb_succ /-
+#print Fin.pred_castSucc_succ /-
 @[simp]
-theorem pred_castSuccEmb_succ (i : Fin n) :
-    pred (castSuccEmb i.succ) (ne_of_gt (castSuccEmb_pos i.succ_pos)) = i.cast_succ := by
+theorem pred_castSucc_succ (i : Fin n) :
+    pred (castSuccEmb i.succ) (ne_of_gt (castSucc_pos i.succ_pos)) = i.cast_succ := by
   simp [eq_iff_veq]
-#align fin.pred_cast_succ_succ Fin.pred_castSuccEmb_succ
+#align fin.pred_cast_succ_succ Fin.pred_castSucc_succ
 -/
 
 #print Fin.addNat_subNat /-
 @[simp]
-theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat m (subNat m i h) = i :=
+theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNatEmb m (subNat m i h) = i :=
   ext <| tsub_add_cancel_of_le h
 #align fin.add_nat_sub_nat Fin.addNat_subNat
 -/
 
 #print Fin.subNat_addNat /-
 @[simp]
-theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addNat m i) :
-    subNat m (addNat m i) h = i :=
+theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNatEmb m i := le_coe_addNat m i) :
+    subNat m (addNatEmb m i) h = i :=
   ext <| add_tsub_cancel_right i m
 #align fin.sub_nat_add_nat Fin.subNat_addNat
 -/
@@ -2024,7 +2024,7 @@ theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addN
 #print Fin.natAdd_subNat_castIso /-
 @[simp]
 theorem natAdd_subNat_castIso {i : Fin (n + m)} (h : n ≤ i) :
-    natAdd n (subNat n (castIso (add_comm _ _) i) h) = i := by simp [← cast_add_nat]
+    natAddEmb n (subNat n (castIso (add_comm _ _) i) h) = i := by simp [← cast_add_nat]
 #align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castIso
 -/
 
@@ -2263,16 +2263,16 @@ theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (F
 #align fin.reverse_induction_last Fin.reverse_induction_last
 -/
 
-#print Fin.reverse_induction_castSuccEmb /-
+#print Fin.reverse_induction_castSucc /-
 @[simp]
-theorem reverse_induction_castSuccEmb {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
+theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) (i : Fin n) :
     (reverseInduction h0 hs i.cast_succ : C i.cast_succ) = hs i (reverseInduction h0 hs i.succ) :=
   by
-  rw [reverse_induction, dif_neg (ne_of_lt (Fin.castSuccEmb_lt_last i))]
+  rw [reverse_induction, dif_neg (ne_of_lt (Fin.castSucc_lt_last i))]
   cases i
   rfl
-#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSuccEmb
+#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSucc
 -/
 
 #print Fin.lastCases /-
@@ -2294,21 +2294,21 @@ theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.la
 #align fin.last_cases_last Fin.lastCases_last
 -/
 
-#print Fin.lastCases_castSuccEmb /-
+#print Fin.lastCases_castSucc /-
 @[simp]
-theorem lastCases_castSuccEmb {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
+theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) (i : Fin n) :
     (Fin.lastCases hlast hcast (Fin.castSuccEmb i) : C (Fin.castSuccEmb i)) = hcast i :=
-  reverse_induction_castSuccEmb _ _ _
-#align fin.last_cases_cast_succ Fin.lastCases_castSuccEmb
+  reverse_induction_castSucc _ _ _
+#align fin.last_cases_cast_succ Fin.lastCases_castSucc
 -/
 
 #print Fin.addCases /-
 /-- Define `f : Π i : fin (m + n), C i` by separately handling the cases `i = cast_add n i`,
 `j : fin m` and `i = nat_add m j`, `j : fin n`. -/
 @[elab_as_elim]
-def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd n i))
-    (hright : ∀ i, C (natAdd m i)) (i : Fin (m + n)) : C i :=
+def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAddEmb n i))
+    (hright : ∀ i, C (natAddEmb m i)) (i : Fin (m + n)) : C i :=
   if hi : (i : ℕ) < m then Eq.recOn (castAdd_castLT n i hi) (hleft (castLT i hi))
   else Eq.recOn (natAdd_subNat_castIso (le_of_not_lt hi)) (hright _)
 #align fin.add_cases Fin.addCases
@@ -2316,9 +2316,9 @@ def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd
 
 #print Fin.addCases_left /-
 @[simp]
-theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
-    (hright : ∀ i, C (natAdd m i)) (i : Fin m) :
-    @addCases _ _ C hleft hright (Fin.castAdd n i) = hleft i :=
+theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAddEmb n i))
+    (hright : ∀ i, C (natAddEmb m i)) (i : Fin m) :
+    @addCases _ _ C hleft hright (Fin.castAddEmb n i) = hleft i :=
   by
   cases' i with i hi
   rw [add_cases, dif_pos (cast_add_lt _ _)]
@@ -2328,9 +2328,9 @@ theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C
 
 #print Fin.addCases_right /-
 @[simp]
-theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
-    (hright : ∀ i, C (natAdd m i)) (i : Fin n) :
-    @addCases _ _ C hleft hright (natAdd m i) = hright i :=
+theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAddEmb n i))
+    (hright : ∀ i, C (natAddEmb m i)) (i : Fin n) :
+    @addCases _ _ C hleft hright (natAddEmb m i) = hright i :=
   by
   have : ¬(nat_add m i : ℕ) < m := (le_coe_nat_add _ _).not_lt
   rw [add_cases, dif_neg this]
@@ -2544,33 +2544,33 @@ end AddGroup
 
 section SuccAbove
 
-#print Fin.succAbove_aux /-
-theorem succAbove_aux (p : Fin (n + 1)) :
+#print Fin.strictMono_succAbove /-
+theorem strictMono_succAbove (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
   (castSuccEmb : Fin n ↪o _).StrictMono.ite (succEmbedding n).StrictMono
     (fun i j hij hj => lt_trans ((castSuccEmb : Fin n ↪o _).lt_iff_lt.2 hij) hj) fun i =>
-    (castSuccEmb_lt_succ i).le
-#align fin.succ_above_aux Fin.succAbove_aux
+    (castSucc_lt_succ i).le
+#align fin.succ_above_aux Fin.strictMono_succAbove
 -/
 
-#print Fin.succAbove /-
+#print Fin.succAboveEmb /-
 /-- `succ_above p i` embeds `fin n` into `fin (n + 1)` with a hole around `p`. -/
-def succAbove (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
-  OrderEmbedding.ofStrictMono _ p.succAbove_aux
-#align fin.succ_above Fin.succAbove
+def succAboveEmb (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
+  OrderEmbedding.ofStrictMono _ p.strictMono_succAbove
+#align fin.succ_above Fin.succAboveEmb
 -/
 
 #print Fin.succAbove_below /-
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
 theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
-    p.succAbove i = i.cast_succ := by rw [succ_above]; exact if_pos h
+    p.succAboveEmb i = i.cast_succ := by rw [succ_above]; exact if_pos h
 #align fin.succ_above_below Fin.succAbove_below
 -/
 
 #print Fin.succAbove_ne_zero_zero /-
 @[simp]
-theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 :=
+theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAboveEmb 0 = 0 :=
   by
   rw [Fin.succAbove_below]
   · rfl
@@ -2580,14 +2580,14 @@ theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.s
 
 #print Fin.succAbove_eq_zero_iff /-
 theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) :
-    a.succAbove b = 0 ↔ b = 0 := by
+    a.succAboveEmb b = 0 ↔ b = 0 := by
   simp only [← succ_above_ne_zero_zero ha, OrderEmbedding.eq_iff_eq]
 #align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iff
 -/
 
 #print Fin.succAbove_ne_zero /-
 theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) (hb : b ≠ 0) :
-    a.succAbove b ≠ 0 :=
+    a.succAboveEmb b ≠ 0 :=
   mt (succAbove_eq_zero_iff ha).mp hb
 #align fin.succ_above_ne_zero Fin.succAbove_ne_zero
 -/
@@ -2595,7 +2595,7 @@ theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0
 #print Fin.succAbove_zero /-
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around zero embeds by `succ`. -/
 @[simp]
-theorem succAbove_zero : ⇑(succAbove (0 : Fin (n + 1))) = Fin.succ :=
+theorem succAbove_zero : ⇑(succAboveEmb (0 : Fin (n + 1))) = Fin.succ :=
   rfl
 #align fin.succ_above_zero Fin.succAbove_zero
 -/
@@ -2603,13 +2603,13 @@ theorem succAbove_zero : ⇑(succAbove (0 : Fin (n + 1))) = Fin.succ :=
 #print Fin.succAbove_last /-
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around `last n` embeds by `cast_succ`. -/
 @[simp]
-theorem succAbove_last : succAbove (Fin.last n) = castSuccEmb := by ext;
+theorem succAbove_last : succAboveEmb (Fin.last n) = castSuccEmb := by ext;
   simp only [succ_above_below, cast_succ_lt_last]
 #align fin.succ_above_last Fin.succAbove_last
 -/
 
 #print Fin.succAbove_last_apply /-
-theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_succ := by
+theorem succAbove_last_apply (i : Fin n) : succAboveEmb (Fin.last n) i = i.cast_succ := by
   rw [succ_above_last]
 #align fin.succ_above_last_apply Fin.succAbove_last_apply
 -/
@@ -2618,7 +2618,7 @@ theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_suc
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
 theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
-    p.succAbove i = i.succ := by simp [succ_above, h.not_lt]
+    p.succAboveEmb i = i.succ := by simp [succ_above, h.not_lt]
 #align fin.succ_above_above Fin.succAbove_above
 -/
 
@@ -2633,7 +2633,7 @@ theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p 
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
   Or.cases_on (succAbove_lt_ge p i) (fun h => Or.inl h) fun h =>
-    Or.inr (lt_of_le_of_lt h (castSuccEmb_lt_succ i))
+    Or.inr (lt_of_le_of_lt h (castSucc_lt_succ i))
 #align fin.succ_above_lt_gt Fin.succAbove_lt_gt
 -/
 
@@ -2641,7 +2641,7 @@ theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p <
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
 @[simp]
-theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i.cast_succ < p :=
+theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAboveEmb i < p ↔ i.cast_succ < p :=
   by
   refine' Iff.intro _ _
   · intro h
@@ -2658,7 +2658,7 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
 #print Fin.lt_succAbove_iff /-
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
-theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p ≤ i.cast_succ :=
+theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAboveEmb i ↔ p ≤ i.cast_succ :=
   by
   refine' Iff.intro _ _
   · intro h
@@ -2675,7 +2675,7 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
 #print Fin.succAbove_ne /-
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 never results in `p` itself -/
-theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
+theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAboveEmb i ≠ p :=
   by
   intro eq
   by_cases H : i.cast_succ < p
@@ -2686,7 +2686,7 @@ theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
 
 #print Fin.succAbove_pos /-
 /-- Embedding a positive `fin n` results in a positive fin (n + 1)` -/
-theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i :=
+theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAboveEmb i :=
   by
   by_cases H : i.cast_succ < p
   · simpa [succ_above_below _ _ H] using cast_succ_pos h
@@ -2697,7 +2697,7 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
 #print Fin.succAbove_castLT /-
 @[simp]
 theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
-    (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLT hx) = x := by
+    (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAboveEmb (x.castLT hx) = x := by
   rw [succ_above_below, cast_succ_cast_lt]; exact h
 #align fin.succ_above_cast_lt Fin.succAbove_castLT
 -/
@@ -2705,27 +2705,27 @@ theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
 #print Fin.succAbove_pred /-
 @[simp]
 theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
-    x.succAbove (y.pred hy) = y := by rw [succ_above_above, succ_pred];
+    x.succAboveEmb (y.pred hy) = y := by rw [succ_above_above, succ_pred];
   simpa [le_iff_coe_le_coe] using Nat.le_pred_of_lt h
 #align fin.succ_above_pred Fin.succAbove_pred
 -/
 
 #print Fin.castLT_succAbove /-
 theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSuccEmb x < y)
-    (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
-    (y.succAbove x).castLT h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
+    (h' : (y.succAboveEmb x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
+    (y.succAboveEmb x).castLT h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
 #align fin.cast_lt_succ_above Fin.castLT_succAbove
 -/
 
 #print Fin.pred_succAbove /-
 theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSuccEmb x)
-    (h' : y.succAbove x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
-    (y.succAbove x).pred h' = x := by simp only [succ_above_above _ _ h, pred_succ]
+    (h' : y.succAboveEmb x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
+    (y.succAboveEmb x).pred h' = x := by simp only [succ_above_above _ _ h, pred_succ]
 #align fin.pred_succ_above Fin.pred_succAbove
 -/
 
 #print Fin.exists_succAbove_eq /-
-theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x :=
+theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAboveEmb z = x :=
   by
   cases' h.lt_or_lt with hlt hlt
   exacts [⟨_, succ_above_cast_lt hlt⟩, ⟨_, succ_above_pred hlt⟩]
@@ -2734,7 +2734,7 @@ theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbo
 
 #print Fin.exists_succAbove_eq_iff /-
 @[simp]
-theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y) ↔ y ≠ x :=
+theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAboveEmb z = y) ↔ y ≠ x :=
   by
   refine' ⟨_, exists_succ_above_eq⟩
   rintro ⟨y, rfl⟩
@@ -2745,7 +2745,7 @@ theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y)
 #print Fin.range_succAbove /-
 /-- The range of `p.succ_above` is everything except `p`. -/
 @[simp]
-theorem range_succAbove (p : Fin (n + 1)) : Set.range p.succAbove = {p}ᶜ :=
+theorem range_succAbove (p : Fin (n + 1)) : Set.range p.succAboveEmb = {p}ᶜ :=
   Set.ext fun _ => exists_succAbove_eq_iff
 #align fin.range_succ_above Fin.range_succAbove
 -/
@@ -2766,21 +2766,21 @@ theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠
 
 #print Fin.succAbove_right_injective /-
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
-theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
-  (succAbove x).Injective
+theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAboveEmb x) :=
+  (succAboveEmb x).Injective
 #align fin.succ_above_right_injective Fin.succAbove_right_injective
 -/
 
 #print Fin.succAbove_right_inj /-
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
-theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b ↔ a = b :=
+theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAboveEmb a = x.succAboveEmb b ↔ a = b :=
   succAbove_right_injective.eq_iff
 #align fin.succ_above_right_inj Fin.succAbove_right_inj
 -/
 
 #print Fin.succAbove_left_injective /-
 /-- `succ_above` is injective at the pivot -/
-theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
+theorem succAbove_left_injective : Injective (@succAboveEmb n) := fun _ _ h => by
   simpa [range_succ_above] using congr_arg (fun f : Fin n ↪o Fin (n + 1) => Set.range fᶜ) h
 #align fin.succ_above_left_injective Fin.succAbove_left_injective
 -/
@@ -2788,21 +2788,21 @@ theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
 #print Fin.succAbove_left_inj /-
 /-- `succ_above` is injective at the pivot -/
 @[simp]
-theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAbove = y.succAbove ↔ x = y :=
+theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAboveEmb = y.succAboveEmb ↔ x = y :=
   succAbove_left_injective.eq_iff
 #align fin.succ_above_left_inj Fin.succAbove_left_inj
 -/
 
 #print Fin.zero_succAbove /-
 @[simp]
-theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i.succ :=
+theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAboveEmb i = i.succ :=
   rfl
 #align fin.zero_succ_above Fin.zero_succAbove
 -/
 
 #print Fin.succ_succAbove_zero /-
 @[simp]
-theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove 0 = 0 :=
+theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAboveEmb 0 = 0 :=
   succAbove_below _ _ (succ_pos _)
 #align fin.succ_succ_above_zero Fin.succ_succAbove_zero
 -/
@@ -2810,7 +2810,7 @@ theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove
 #print Fin.succ_succAbove_succ /-
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
-    i.succ.succAbove j.succ = (i.succAbove j).succ :=
+    i.succ.succAboveEmb j.succ = (i.succAboveEmb j).succ :=
   (lt_or_ge j.cast_succ i).elim
     (fun h => by
       have h' : j.succ.cast_succ < i.succ := by simpa [lt_iff_coe_lt_coe] using h
@@ -2825,7 +2825,7 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
 
 #print Fin.one_succAbove_zero /-
 @[simp]
-theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
+theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAboveEmb 0 = 0 :=
   succ_succAbove_zero 0
 #align fin.one_succ_above_zero Fin.one_succAbove_zero
 -/
@@ -2835,21 +2835,22 @@ theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
 simplification using `succ_above_zero` or `succ_succ_above_zero`. -/
 @[simp]
 theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
-    i.succ.succAbove 1 = (i.succAbove 0).succ := by
+    i.succ.succAboveEmb 1 = (i.succAboveEmb 0).succ := by
   rw [← succ_succ_above_succ i 0, succ_zero_eq_one]
 #align fin.succ_succ_above_one Fin.succ_succAbove_one
 -/
 
 #print Fin.one_succAbove_succ /-
 @[simp]
-theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j.succ = j.succ.succ :=
+theorem one_succAbove_succ {n : ℕ} (j : Fin n) :
+    (1 : Fin (n + 2)).succAboveEmb j.succ = j.succ.succ :=
   succ_succAbove_succ 0 j
 #align fin.one_succ_above_succ Fin.one_succAbove_succ
 -/
 
 #print Fin.one_succAbove_one /-
 @[simp]
-theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 :=
+theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAboveEmb 1 = 2 :=
   succ_succAbove_succ 0 0
 #align fin.one_succ_above_one Fin.one_succAbove_one
 -/
@@ -2990,7 +2991,7 @@ theorem castPred_monotone : Monotone (@castPred n) :=
 then back to `fin (n+1)` with a gap around `p` is the identity away from `p`. -/
 @[simp]
 theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ) :
-    p.cast_succ.succAbove (p.predAbove i) = i :=
+    p.cast_succ.succAboveEmb (p.predAbove i) = i :=
   by
   dsimp [pred_above, succ_above]
   rcases p with ⟨p, _⟩
@@ -3002,7 +3003,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
     -- For some reason `simp` doesn't fire fully unless we discharge the third goal.
     · exact lt_of_le_of_ne H (Ne.symm h)
     · simp
-    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSuccEmb_mk] at h 
+    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSucc_mk] at h 
       simp only [pred, Fin.mk_lt_mk, not_lt]
       exact Nat.le_pred_of_lt (Nat.lt_of_le_and_ne H (Ne.symm h))
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
@@ -3012,7 +3013,8 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
 /-- Sending `fin n` into `fin (n + 1)` with a gap at `p`
 then back to `fin n` by subtracting one from anything above `p` is the identity. -/
 @[simp]
-theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.succAbove i) = i :=
+theorem predAbove_succAbove (p : Fin n) (i : Fin n) :
+    p.predAbove (p.cast_succ.succAboveEmb i) = i :=
   by
   dsimp [pred_above, succ_above]
   rcases p with ⟨p, _⟩
@@ -3030,17 +3032,18 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
 #align fin.pred_above_succ_above Fin.predAbove_succAbove
 -/
 
-#print Fin.castSuccEmb_pred_eq_pred_castSuccEmb /-
-theorem castSuccEmb_pred_eq_pred_castSuccEmb {a : Fin (n + 1)} (ha : a ≠ 0)
-    (ha' := a.castSuccEmb_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' := by
+#print Fin.castSucc_pred_eq_pred_castSucc /-
+theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
+    (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' := by
   cases a; rfl
-#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSuccEmb_pred_eq_pred_castSuccEmb
+#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSucc
 -/
 
 #print Fin.pred_succAbove_pred /-
 /-- `pred` commutes with `succ_above`. -/
 theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
-    (hk := succAbove_ne_zero ha hb) : (a.pred ha).succAbove (b.pred hb) = (a.succAbove b).pred hk :=
+    (hk := succAbove_ne_zero ha hb) :
+    (a.pred ha).succAboveEmb (b.pred hb) = (a.succAboveEmb b).pred hk :=
   by
   obtain hbelow | habove := lt_or_le b.cast_succ a
   -- `rwa` uses them
@@ -3062,8 +3065,8 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
   by
   obtain h₁ | h₂ := lt_or_le a.cast_succ b
   · rw [Fin.predAbove_above _ _ h₁, Fin.succ_pred, Fin.predAbove_above, Fin.pred_succ]
-    simpa only [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ,
-      add_lt_add_iff_right] using h₁
+    simpa only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, add_lt_add_iff_right] using
+      h₁
   · cases n
     · exfalso
       exact not_lt_zero' a.is_lt
@@ -3084,20 +3087,20 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ
 -/
 
-#print Fin.castPred_castSuccEmb /-
+#print Fin.castPred_castSucc /-
 @[simp]
-theorem castPred_castSuccEmb (i : Fin (n + 1)) : castPred i.cast_succ = i := by
+theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
   simp [cast_pred, pred_above, le_last]
-#align fin.cast_pred_cast_succ Fin.castPred_castSuccEmb
+#align fin.cast_pred_cast_succ Fin.castPred_castSucc
 -/
 
-#print Fin.castSuccEmb_castPred /-
-theorem castSuccEmb_castPred {i : Fin (n + 2)} (h : i < last _) : castSuccEmb i.cast_pred = i :=
+#print Fin.castSucc_castPred /-
+theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSuccEmb i.cast_pred = i :=
   by
   rw [cast_pred, pred_above, dif_neg]
   · simp [Fin.eq_iff_veq]
   · exact h.not_le
-#align fin.cast_succ_cast_pred Fin.castSuccEmb_castPred
+#align fin.cast_succ_cast_pred Fin.castSucc_castPred
 -/
 
 #print Fin.coe_castPred_le_self /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/b01d6eb9d0a308807af54319b264d0994b91774b

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Keeley Hoek
 
 ! This file was ported from Lean 3 source module data.fin.basic
-! leanprover-community/mathlib commit f2f413b9d4be3a02840d0663dace76e8fe3da053
+! leanprover-community/mathlib commit 3a2b5524a138b5d0b818b858b516d4ac8a484b03
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -807,6 +807,13 @@ theorem subsingleton_iff_le_one : Subsingleton (Fin n) ↔ n ≤ 1 := by
 
 section Monoid
 
+instance addCommSemigroup (n : ℕ) : AddCommSemigroup (Fin n)
+    where
+  add := (· + ·)
+  add_assoc := by simp [eq_iff_veq, add_def, add_assoc]
+  add_comm := by simp [eq_iff_veq, add_def, add_comm]
+#align fin.add_comm_semigroup Fin.addCommSemigroup
+
 #print Fin.add_zero /-
 @[simp]
 protected theorem add_zero [NeZero n] (k : Fin n) : k + 0 = k := by
@@ -822,14 +829,12 @@ protected theorem zero_add [NeZero n] (k : Fin n) : (0 : Fin n) + k = k := by
 -/
 
 #print Fin.addCommMonoid /-
-instance addCommMonoid (n : ℕ) [NeZero n] : AddCommMonoid (Fin n)
-    where
-  add := (· + ·)
-  add_assoc := by simp [eq_iff_veq, add_def, add_assoc]
-  zero := 0
-  zero_add := Fin.zero_add
-  add_zero := Fin.add_zero
-  add_comm := by simp [eq_iff_veq, add_def, add_comm]
+instance addCommMonoid (n : ℕ) [NeZero n] : AddCommMonoid (Fin n) :=
+  { Fin.addCommSemigroup n with
+    add := (· + ·)
+    zero := 0
+    zero_add := Fin.zero_add
+    add_zero := Fin.add_zero }
 #align fin.add_comm_monoid Fin.addCommMonoid
 -/
 
@@ -2407,6 +2412,26 @@ instance (n : ℕ) [NeZero n] : AddCommGroup (Fin n) :=
       Fin.ext <| show (a + (n - b)) % n = (a + (n - b) % n) % n by simp
     sub := Fin.sub }
 
+/-- Note this is more general than `fin.add_comm_group` as it applies (vacuously) to `fin 0` too. -/
+instance (n : ℕ) : InvolutiveNeg (Fin n)
+    where
+  neg := Neg.neg
+  neg_neg := Nat.casesOn n finZeroElim fun i => neg_neg
+
+/-- Note this is more general than `fin.add_comm_group` as it applies (vacuously) to `fin 0` too. -/
+instance (n : ℕ) : IsCancelAdd (Fin n)
+    where
+  add_left_cancel := Nat.casesOn n finZeroElim fun i _ _ _ => add_left_cancel
+  add_right_cancel := Nat.casesOn n finZeroElim fun i _ _ _ => add_right_cancel
+
+/-- Note this is more general than `fin.add_comm_group` as it applies (vacuously) to `fin 0` too. -/
+instance (n : ℕ) : AddLeftCancelSemigroup (Fin n) :=
+  { Fin.addCommSemigroup n, Fin.isCancelAdd n with }
+
+/-- Note this is more general than `fin.add_comm_group` as it applies (vacuously) to `fin 0` too. -/
+instance (n : ℕ) : AddRightCancelSemigroup (Fin n) :=
+  { Fin.addCommSemigroup n, Fin.isCancelAdd n with }
+
 #print Fin.coe_neg /-
 protected theorem coe_neg (a : Fin n) : ((-a : Fin n) : ℕ) = (n - a) % n :=
   rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

@@ -1506,53 +1506,53 @@ theorem succ_castIso_eq {n' : ℕ} (i : Fin n) (h : n = n') :
 #align fin.succ_cast_eq Fin.succ_castIso_eq
 -/
 
-#print Fin.castSucc /-
+#print Fin.castSuccEmb /-
 /-- `cast_succ i` embeds `i : fin n` in `fin (n+1)`. -/
-def castSucc : Fin n ↪o Fin (n + 1) :=
+def castSuccEmb : Fin n ↪o Fin (n + 1) :=
   castAdd 1
-#align fin.cast_succ Fin.castSucc
+#align fin.cast_succ Fin.castSuccEmb
 -/
 
-#print Fin.coe_castSucc /-
+#print Fin.coe_castSuccEmb /-
 @[simp]
-theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
+theorem coe_castSuccEmb (i : Fin n) : (i.cast_succ : ℕ) = i :=
   rfl
-#align fin.coe_cast_succ Fin.coe_castSucc
+#align fin.coe_cast_succ Fin.coe_castSuccEmb
 -/
 
-#print Fin.castSucc_mk /-
+#print Fin.castSuccEmb_mk /-
 @[simp]
-theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
+theorem castSuccEmb_mk (n i : ℕ) (h : i < n) : castSuccEmb ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
   rfl
-#align fin.cast_succ_mk Fin.castSucc_mk
+#align fin.cast_succ_mk Fin.castSuccEmb_mk
 -/
 
-#print Fin.castIso_castSucc /-
+#print Fin.castIso_castSuccEmb /-
 @[simp]
-theorem castIso_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
-    castIso h (castSucc i) = castSucc (castIso (Nat.succ_injective h) i) := by ext;
+theorem castIso_castSuccEmb {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
+    castIso h (castSuccEmb i) = castSuccEmb (castIso (Nat.succ_injective h) i) := by ext;
   simp only [coe_cast, coe_cast_succ]
-#align fin.cast_cast_succ Fin.castIso_castSucc
+#align fin.cast_cast_succ Fin.castIso_castSuccEmb
 -/
 
-#print Fin.castSucc_lt_succ /-
-theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
+#print Fin.castSuccEmb_lt_succ /-
+theorem castSuccEmb_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
   lt_iff_val_lt_val.2 <| by simp only [coe_cast_succ, coe_succ, Nat.lt_succ_self]
-#align fin.cast_succ_lt_succ Fin.castSucc_lt_succ
+#align fin.cast_succ_lt_succ Fin.castSuccEmb_lt_succ
 -/
 
-#print Fin.le_castSucc_iff /-
-theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
+#print Fin.le_castSuccEmb_iff /-
+theorem le_castSuccEmb_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
   simpa [lt_iff_coe_lt_coe, le_iff_coe_le_coe] using nat.succ_le_succ_iff.symm
-#align fin.le_cast_succ_iff Fin.le_castSucc_iff
+#align fin.le_cast_succ_iff Fin.le_castSuccEmb_iff
 -/
 
-#print Fin.castSucc_lt_iff_succ_le /-
-theorem castSucc_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
+#print Fin.castSuccEmb_lt_iff_succ_le /-
+theorem castSuccEmb_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
     i.cast_succ < j ↔ i.succ ≤ j := by
-  simpa only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc] using
+  simpa only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSuccEmb] using
     Nat.lt_iff_add_one_le
-#align fin.cast_succ_lt_iff_succ_le Fin.castSucc_lt_iff_succ_le
+#align fin.cast_succ_lt_iff_succ_le Fin.castSuccEmb_lt_iff_succ_le
 -/
 
 #print Fin.succ_last /-
@@ -1569,92 +1569,92 @@ theorem succ_eq_last_succ {n : ℕ} (i : Fin n.succ) : i.succ = last (n + 1) ↔
 #align fin.succ_eq_last_succ Fin.succ_eq_last_succ
 -/
 
-#print Fin.castSucc_castLT /-
+#print Fin.castSuccEmb_castLT /-
 @[simp]
-theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT i h) = i :=
+theorem castSuccEmb_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSuccEmb (castLT i h) = i :=
   Fin.eq_of_veq rfl
-#align fin.cast_succ_cast_lt Fin.castSucc_castLT
+#align fin.cast_succ_cast_lt Fin.castSuccEmb_castLT
 -/
 
-#print Fin.castLT_castSucc /-
+#print Fin.castLT_castSuccEmb /-
 @[simp]
-theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSucc a) h = a := by
-  cases a <;> rfl
-#align fin.cast_lt_cast_succ Fin.castLT_castSucc
+theorem castLT_castSuccEmb {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSuccEmb a) h = a :=
+  by cases a <;> rfl
+#align fin.cast_lt_cast_succ Fin.castLT_castSuccEmb
 -/
 
-#print Fin.castSucc_lt_castSucc_iff /-
+#print Fin.castSuccEmb_lt_castSuccEmb_iff /-
 @[simp]
-theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
-  (@castSucc n).lt_iff_lt
-#align fin.cast_succ_lt_cast_succ_iff Fin.castSucc_lt_castSucc_iff
+theorem castSuccEmb_lt_castSuccEmb_iff : a.cast_succ < b.cast_succ ↔ a < b :=
+  (@castSuccEmb n).lt_iff_lt
+#align fin.cast_succ_lt_cast_succ_iff Fin.castSuccEmb_lt_castSuccEmb_iff
 -/
 
-#print Fin.castSucc_injective /-
-theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
-  (castSucc : Fin n ↪o _).Injective
-#align fin.cast_succ_injective Fin.castSucc_injective
+#print Fin.castSuccEmb_injective /-
+theorem castSuccEmb_injective (n : ℕ) : Injective (@Fin.castSuccEmb n) :=
+  (castSuccEmb : Fin n ↪o _).Injective
+#align fin.cast_succ_injective Fin.castSuccEmb_injective
 -/
 
-#print Fin.castSucc_inj /-
-theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
-  (castSucc_injective n).eq_iff
-#align fin.cast_succ_inj Fin.castSucc_inj
+#print Fin.castSuccEmb_inj /-
+theorem castSuccEmb_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
+  (castSuccEmb_injective n).eq_iff
+#align fin.cast_succ_inj Fin.castSuccEmb_inj
 -/
 
-#print Fin.castSucc_lt_last /-
-theorem castSucc_lt_last (a : Fin n) : castSucc a < last n :=
+#print Fin.castSuccEmb_lt_last /-
+theorem castSuccEmb_lt_last (a : Fin n) : castSuccEmb a < last n :=
   lt_iff_val_lt_val.mpr a.is_lt
-#align fin.cast_succ_lt_last Fin.castSucc_lt_last
+#align fin.cast_succ_lt_last Fin.castSuccEmb_lt_last
 -/
 
-#print Fin.castSucc_zero /-
+#print Fin.castSuccEmb_zero /-
 @[simp]
-theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
+theorem castSuccEmb_zero [NeZero n] : castSuccEmb (0 : Fin n) = 0 :=
   rfl
-#align fin.cast_succ_zero Fin.castSucc_zero
+#align fin.cast_succ_zero Fin.castSuccEmb_zero
 -/
 
-#print Fin.castSucc_one /-
+#print Fin.castSuccEmb_one /-
 @[simp]
-theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
+theorem castSuccEmb_one {n : ℕ} : Fin.castSuccEmb (1 : Fin (n + 2)) = 1 :=
   rfl
-#align fin.cast_succ_one Fin.castSucc_one
+#align fin.cast_succ_one Fin.castSuccEmb_one
 -/
 
-#print Fin.castSucc_pos /-
+#print Fin.castSuccEmb_pos /-
 /-- `cast_succ i` is positive when `i` is positive -/
-theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
+theorem castSuccEmb_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSuccEmb i := by
   simpa [lt_iff_coe_lt_coe] using h
-#align fin.cast_succ_pos Fin.castSucc_pos
+#align fin.cast_succ_pos Fin.castSuccEmb_pos
 -/
 
-#print Fin.castSucc_eq_zero_iff /-
+#print Fin.castSuccEmb_eq_zero_iff /-
 @[simp]
-theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
+theorem castSuccEmb_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
   Fin.ext_iff.trans <| (Fin.ext_iff.trans <| Iff.rfl).symm
-#align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iff
+#align fin.cast_succ_eq_zero_iff Fin.castSuccEmb_eq_zero_iff
 -/
 
-#print Fin.castSucc_ne_zero_iff /-
-theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
-  not_iff_not.mpr <| castSucc_eq_zero_iff a
-#align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iff
+#print Fin.castSuccEmb_ne_zero_iff /-
+theorem castSuccEmb_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
+  not_iff_not.mpr <| castSuccEmb_eq_zero_iff a
+#align fin.cast_succ_ne_zero_iff Fin.castSuccEmb_ne_zero_iff
 -/
 
-#print Fin.castSucc_fin_succ /-
-theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.succ (castSucc j) := by
-  simp [Fin.ext_iff]
-#align fin.cast_succ_fin_succ Fin.castSucc_fin_succ
+#print Fin.castSuccEmb_fin_succ /-
+theorem castSuccEmb_fin_succ (n : ℕ) (j : Fin n) :
+    castSuccEmb (Fin.succ j) = Fin.succ (castSuccEmb j) := by simp [Fin.ext_iff]
+#align fin.cast_succ_fin_succ Fin.castSuccEmb_fin_succ
 -/
 
-#print Fin.coe_eq_castSucc /-
+#print Fin.coe_eq_castSuccEmb /-
 @[norm_cast, simp]
-theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
+theorem coe_eq_castSuccEmb : (a : Fin (n + 1)) = a.cast_succ :=
   by
   ext
   exact coe_val_of_lt (Nat.lt.step a.is_lt)
-#align fin.coe_eq_cast_succ Fin.coe_eq_castSucc
+#align fin.coe_eq_cast_succ Fin.coe_eq_castSuccEmb
 -/
 
 #print Fin.coeSucc_eq_succ /-
@@ -1673,27 +1673,28 @@ theorem lt_succ : a.cast_succ < a.succ := by
 #align fin.lt_succ Fin.lt_succ
 -/
 
-#print Fin.range_castSucc /-
+#print Fin.range_castSuccEmb /-
 @[simp]
-theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = {i | (i : ℕ) < n} :=
+theorem range_castSuccEmb {n : ℕ} :
+    Set.range (castSuccEmb : Fin n → Fin n.succ) = {i | (i : ℕ) < n} :=
   range_castLE _
-#align fin.range_cast_succ Fin.range_castSucc
+#align fin.range_cast_succ Fin.range_castSuccEmb
 -/
 
-#print Fin.coe_of_injective_castSucc_symm /-
+#print Fin.coe_of_injective_castSuccEmb_symm /-
 @[simp]
-theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
-    ((Equiv.ofInjective castSucc (castSucc_injective _)).symm ⟨i, hi⟩ : ℕ) = i :=
+theorem coe_of_injective_castSuccEmb_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
+    ((Equiv.ofInjective castSuccEmb (castSuccEmb_injective _)).symm ⟨i, hi⟩ : ℕ) = i :=
   by
   rw [← coe_cast_succ]
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
-#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symm
+#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSuccEmb_symm
 -/
 
-#print Fin.succ_castSucc /-
-theorem succ_castSucc {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
+#print Fin.succ_castSuccEmb /-
+theorem succ_castSuccEmb {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
   Fin.ext (by simp)
-#align fin.succ_cast_succ Fin.succ_castSucc
+#align fin.succ_cast_succ Fin.succ_castSuccEmb
 -/
 
 #print Fin.addNat /-
@@ -1870,10 +1871,11 @@ theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
 #align fin.nat_add_last Fin.natAdd_last
 -/
 
-#print Fin.natAdd_castSucc /-
-theorem natAdd_castSucc {m n : ℕ} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
+#print Fin.natAdd_castSuccEmb /-
+theorem natAdd_castSuccEmb {m n : ℕ} {i : Fin m} :
+    natAdd n (castSuccEmb i) = castSuccEmb (natAdd n i) :=
   rfl
-#align fin.nat_add_cast_succ Fin.natAdd_castSucc
+#align fin.nat_add_cast_succ Fin.natAdd_castSuccEmb
 -/
 
 end Succ
@@ -1991,12 +1993,12 @@ theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
 #align fin.sub_nat_mk Fin.subNat_mk
 -/
 
-#print Fin.pred_castSucc_succ /-
+#print Fin.pred_castSuccEmb_succ /-
 @[simp]
-theorem pred_castSucc_succ (i : Fin n) :
-    pred (castSucc i.succ) (ne_of_gt (castSucc_pos i.succ_pos)) = i.cast_succ := by
+theorem pred_castSuccEmb_succ (i : Fin n) :
+    pred (castSuccEmb i.succ) (ne_of_gt (castSuccEmb_pos i.succ_pos)) = i.cast_succ := by
   simp [eq_iff_veq]
-#align fin.pred_cast_succ_succ Fin.pred_castSucc_succ
+#align fin.pred_cast_succ_succ Fin.pred_castSuccEmb_succ
 -/
 
 #print Fin.addNat_subNat /-
@@ -2241,7 +2243,7 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
       have wf : n + 1 - j.succ < n + 1 - i := by
         cases i
         rw [tsub_lt_tsub_iff_left_of_le] <;> simp [*, Nat.succ_le_iff]
-      have hi : i = Fin.castSucc j := Fin.ext rfl
+      have hi : i = Fin.castSuccEmb j := Fin.ext rfl
       cast (by rw [hi]) (hs _ (reverse_induction j.succ))
 termination_by' ⟨_, measure_wf fun i : Fin (n + 1) => n + 1 - i⟩
 #align fin.reverse_induction Fin.reverseInduction
@@ -2256,16 +2258,16 @@ theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (F
 #align fin.reverse_induction_last Fin.reverse_induction_last
 -/
 
-#print Fin.reverse_induction_castSucc /-
+#print Fin.reverse_induction_castSuccEmb /-
 @[simp]
-theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
+theorem reverse_induction_castSuccEmb {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) (i : Fin n) :
     (reverseInduction h0 hs i.cast_succ : C i.cast_succ) = hs i (reverseInduction h0 hs i.succ) :=
   by
-  rw [reverse_induction, dif_neg (ne_of_lt (Fin.castSucc_lt_last i))]
+  rw [reverse_induction, dif_neg (ne_of_lt (Fin.castSuccEmb_lt_last i))]
   cases i
   rfl
-#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSucc
+#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSuccEmb
 -/
 
 #print Fin.lastCases /-
@@ -2287,13 +2289,13 @@ theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.la
 #align fin.last_cases_last Fin.lastCases_last
 -/
 
-#print Fin.lastCases_castSucc /-
+#print Fin.lastCases_castSuccEmb /-
 @[simp]
-theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
+theorem lastCases_castSuccEmb {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) (i : Fin n) :
-    (Fin.lastCases hlast hcast (Fin.castSucc i) : C (Fin.castSucc i)) = hcast i :=
-  reverse_induction_castSucc _ _ _
-#align fin.last_cases_cast_succ Fin.lastCases_castSucc
+    (Fin.lastCases hlast hcast (Fin.castSuccEmb i) : C (Fin.castSuccEmb i)) = hcast i :=
+  reverse_induction_castSuccEmb _ _ _
+#align fin.last_cases_cast_succ Fin.lastCases_castSuccEmb
 -/
 
 #print Fin.addCases /-
@@ -2520,9 +2522,9 @@ section SuccAbove
 #print Fin.succAbove_aux /-
 theorem succAbove_aux (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
-  (castSucc : Fin n ↪o _).StrictMono.ite (succEmbedding n).StrictMono
-    (fun i j hij hj => lt_trans ((castSucc : Fin n ↪o _).lt_iff_lt.2 hij) hj) fun i =>
-    (castSucc_lt_succ i).le
+  (castSuccEmb : Fin n ↪o _).StrictMono.ite (succEmbedding n).StrictMono
+    (fun i j hij hj => lt_trans ((castSuccEmb : Fin n ↪o _).lt_iff_lt.2 hij) hj) fun i =>
+    (castSuccEmb_lt_succ i).le
 #align fin.succ_above_aux Fin.succAbove_aux
 -/
 
@@ -2576,7 +2578,7 @@ theorem succAbove_zero : ⇑(succAbove (0 : Fin (n + 1))) = Fin.succ :=
 #print Fin.succAbove_last /-
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around `last n` embeds by `cast_succ`. -/
 @[simp]
-theorem succAbove_last : succAbove (Fin.last n) = castSucc := by ext;
+theorem succAbove_last : succAbove (Fin.last n) = castSuccEmb := by ext;
   simp only [succ_above_below, cast_succ_lt_last]
 #align fin.succ_above_last Fin.succAbove_last
 -/
@@ -2598,7 +2600,7 @@ theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
 #print Fin.succAbove_lt_ge /-
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p ≤ i.cast_succ :=
-  lt_or_ge (castSucc i) p
+  lt_or_ge (castSuccEmb i) p
 #align fin.succ_above_lt_ge Fin.succAbove_lt_ge
 -/
 
@@ -2606,7 +2608,7 @@ theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p 
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
   Or.cases_on (succAbove_lt_ge p i) (fun h => Or.inl h) fun h =>
-    Or.inr (lt_of_le_of_lt h (castSucc_lt_succ i))
+    Or.inr (lt_of_le_of_lt h (castSuccEmb_lt_succ i))
 #align fin.succ_above_lt_gt Fin.succAbove_lt_gt
 -/
 
@@ -2684,14 +2686,14 @@ theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_
 -/
 
 #print Fin.castLT_succAbove /-
-theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
+theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSuccEmb x < y)
     (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
     (y.succAbove x).castLT h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
 #align fin.cast_lt_succ_above Fin.castLT_succAbove
 -/
 
 #print Fin.pred_succAbove /-
-theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
+theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSuccEmb x)
     (h' : y.succAbove x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
     (y.succAbove x).pred h' = x := by simp only [succ_above_above _ _ h, pred_succ]
 #align fin.pred_succ_above Fin.pred_succAbove
@@ -2975,7 +2977,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
     -- For some reason `simp` doesn't fire fully unless we discharge the third goal.
     · exact lt_of_le_of_ne H (Ne.symm h)
     · simp
-    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSucc_mk] at h 
+    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSuccEmb_mk] at h 
       simp only [pred, Fin.mk_lt_mk, not_lt]
       exact Nat.le_pred_of_lt (Nat.lt_of_le_and_ne H (Ne.symm h))
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
@@ -3003,11 +3005,11 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
 #align fin.pred_above_succ_above Fin.predAbove_succAbove
 -/
 
-#print Fin.castSucc_pred_eq_pred_castSucc /-
-theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
-    (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' := by
+#print Fin.castSuccEmb_pred_eq_pred_castSuccEmb /-
+theorem castSuccEmb_pred_eq_pred_castSuccEmb {a : Fin (n + 1)} (ha : a ≠ 0)
+    (ha' := a.castSuccEmb_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' := by
   cases a; rfl
-#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSucc
+#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSuccEmb_pred_eq_pred_castSuccEmb
 -/
 
 #print Fin.pred_succAbove_pred /-
@@ -3035,8 +3037,8 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
   by
   obtain h₁ | h₂ := lt_or_le a.cast_succ b
   · rw [Fin.predAbove_above _ _ h₁, Fin.succ_pred, Fin.predAbove_above, Fin.pred_succ]
-    simpa only [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, add_lt_add_iff_right] using
-      h₁
+    simpa only [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ,
+      add_lt_add_iff_right] using h₁
   · cases n
     · exfalso
       exact not_lt_zero' a.is_lt
@@ -3057,20 +3059,20 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ
 -/
 
-#print Fin.castPred_castSucc /-
+#print Fin.castPred_castSuccEmb /-
 @[simp]
-theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
+theorem castPred_castSuccEmb (i : Fin (n + 1)) : castPred i.cast_succ = i := by
   simp [cast_pred, pred_above, le_last]
-#align fin.cast_pred_cast_succ Fin.castPred_castSucc
+#align fin.cast_pred_cast_succ Fin.castPred_castSuccEmb
 -/
 
-#print Fin.castSucc_castPred /-
-theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSucc i.cast_pred = i :=
+#print Fin.castSuccEmb_castPred /-
+theorem castSuccEmb_castPred {i : Fin (n + 2)} (h : i < last _) : castSuccEmb i.cast_pred = i :=
   by
   rw [cast_pred, pred_above, dif_neg]
   · simp [Fin.eq_iff_veq]
   · exact h.not_le
-#align fin.cast_succ_cast_pred Fin.castSucc_castPred
+#align fin.cast_succ_cast_pred Fin.castSuccEmb_castPred
 -/
 
 #print Fin.coe_castPred_le_self /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

@@ -517,71 +517,71 @@ theorem eq_succ_of_ne_zero {n : ℕ} {i : Fin (n + 1)} (hi : i ≠ 0) : ∃ j :
 #align fin.eq_succ_of_ne_zero Fin.eq_succ_of_ne_zero
 -/
 
-#print Fin.rev /-
+#print Fin.revPerm /-
 /-- The antitone involution `fin n → fin n` given by `i ↦ n-(i+1)`. -/
-def rev : Equiv.Perm (Fin n) :=
+def revPerm : Equiv.Perm (Fin n) :=
   Involutive.toPerm (fun i => ⟨n - (i + 1), tsub_lt_self i.Pos (Nat.succ_pos _)⟩) fun i =>
     ext <| by
       rw [coe_mk, coe_mk, ← tsub_tsub, tsub_tsub_cancel_of_le (Nat.add_one_le_iff.2 i.is_lt),
         add_tsub_cancel_right]
-#align fin.rev Fin.rev
+#align fin.rev Fin.revPerm
 -/
 
-#print Fin.val_rev /-
+#print Fin.val_revPerm /-
 @[simp]
-theorem val_rev (i : Fin n) : (i.rev : ℕ) = n - (i + 1) :=
+theorem val_revPerm (i : Fin n) : (i.revPerm : ℕ) = n - (i + 1) :=
   rfl
-#align fin.coe_rev Fin.val_rev
+#align fin.coe_rev Fin.val_revPerm
 -/
 
-#print Fin.rev_involutive /-
-theorem rev_involutive : Involutive (@rev n) :=
+#print Fin.revPerm_involutive /-
+theorem revPerm_involutive : Involutive (@revPerm n) :=
   Involutive.toPerm_involutive _
-#align fin.rev_involutive Fin.rev_involutive
+#align fin.rev_involutive Fin.revPerm_involutive
 -/
 
-#print Fin.rev_injective /-
-theorem rev_injective : Injective (@rev n) :=
-  rev_involutive.Injective
-#align fin.rev_injective Fin.rev_injective
+#print Fin.revPerm_injective /-
+theorem revPerm_injective : Injective (@revPerm n) :=
+  revPerm_involutive.Injective
+#align fin.rev_injective Fin.revPerm_injective
 -/
 
-#print Fin.rev_surjective /-
-theorem rev_surjective : Surjective (@rev n) :=
-  rev_involutive.Surjective
-#align fin.rev_surjective Fin.rev_surjective
+#print Fin.revPerm_surjective /-
+theorem revPerm_surjective : Surjective (@revPerm n) :=
+  revPerm_involutive.Surjective
+#align fin.rev_surjective Fin.revPerm_surjective
 -/
 
-#print Fin.rev_bijective /-
-theorem rev_bijective : Bijective (@rev n) :=
-  rev_involutive.Bijective
-#align fin.rev_bijective Fin.rev_bijective
+#print Fin.revPerm_bijective /-
+theorem revPerm_bijective : Bijective (@revPerm n) :=
+  revPerm_involutive.Bijective
+#align fin.rev_bijective Fin.revPerm_bijective
 -/
 
-#print Fin.rev_inj /-
+#print Fin.revPerm_inj /-
 @[simp]
-theorem rev_inj {i j : Fin n} : i.rev = j.rev ↔ i = j :=
-  rev_injective.eq_iff
-#align fin.rev_inj Fin.rev_inj
+theorem revPerm_inj {i j : Fin n} : i.revPerm = j.revPerm ↔ i = j :=
+  revPerm_injective.eq_iff
+#align fin.rev_inj Fin.revPerm_inj
 -/
 
-#print Fin.rev_rev /-
+#print Fin.revPerm_revPerm /-
 @[simp]
-theorem rev_rev (i : Fin n) : i.rev.rev = i :=
-  rev_involutive _
-#align fin.rev_rev Fin.rev_rev
+theorem revPerm_revPerm (i : Fin n) : i.revPerm.revPerm = i :=
+  revPerm_involutive _
+#align fin.rev_rev Fin.revPerm_revPerm
 -/
 
-#print Fin.rev_symm /-
+#print Fin.revPerm_symm /-
 @[simp]
-theorem rev_symm : (@rev n).symm = rev :=
+theorem revPerm_symm : (@revPerm n).symm = revPerm :=
   rfl
-#align fin.rev_symm Fin.rev_symm
+#align fin.rev_symm Fin.revPerm_symm
 -/
 
-#print Fin.rev_eq /-
-theorem rev_eq {n a : ℕ} (i : Fin (n + 1)) (h : n = a + i) :
-    i.rev = ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro h.symm)⟩ :=
+#print Fin.revPerm_eq /-
+theorem revPerm_eq {n a : ℕ} (i : Fin (n + 1)) (h : n = a + i) :
+    i.revPerm = ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro h.symm)⟩ :=
   by
   ext
   dsimp
@@ -589,35 +589,35 @@ theorem rev_eq {n a : ℕ} (i : Fin (n + 1)) (h : n = a + i) :
     congr
     rw [h]
   rw [add_assoc, add_tsub_cancel_right]
-#align fin.rev_eq Fin.rev_eq
+#align fin.rev_eq Fin.revPerm_eq
 -/
 
-#print Fin.rev_le_rev /-
+#print Fin.revPerm_le_revPerm /-
 @[simp]
-theorem rev_le_rev {i j : Fin n} : i.rev ≤ j.rev ↔ j ≤ i := by
+theorem revPerm_le_revPerm {i j : Fin n} : i.revPerm ≤ j.revPerm ↔ j ≤ i := by
   simp only [le_iff_coe_le_coe, coe_rev, tsub_le_tsub_iff_left (Nat.add_one_le_iff.2 j.is_lt),
     add_le_add_iff_right]
-#align fin.rev_le_rev Fin.rev_le_rev
+#align fin.rev_le_rev Fin.revPerm_le_revPerm
 -/
 
-#print Fin.rev_lt_rev /-
+#print Fin.revPerm_lt_revPerm /-
 @[simp]
-theorem rev_lt_rev {i j : Fin n} : i.rev < j.rev ↔ j < i :=
-  lt_iff_lt_of_le_iff_le rev_le_rev
-#align fin.rev_lt_rev Fin.rev_lt_rev
+theorem revPerm_lt_revPerm {i j : Fin n} : i.revPerm < j.revPerm ↔ j < i :=
+  lt_iff_lt_of_le_iff_le revPerm_le_revPerm
+#align fin.rev_lt_rev Fin.revPerm_lt_revPerm
 -/
 
 #print Fin.revOrderIso /-
 /-- `fin.rev n` as an order-reversing isomorphism. -/
 @[simps apply toEquiv]
 def revOrderIso {n} : (Fin n)ᵒᵈ ≃o Fin n :=
-  ⟨OrderDual.ofDual.trans rev, fun i j => rev_le_rev⟩
+  ⟨OrderDual.ofDual.trans revPerm, fun i j => revPerm_le_revPerm⟩
 #align fin.rev_order_iso Fin.revOrderIso
 -/
 
 #print Fin.revOrderIso_symm_apply /-
 @[simp]
-theorem revOrderIso_symm_apply (i : Fin n) : revOrderIso.symm i = OrderDual.toDual i.rev :=
+theorem revOrderIso_symm_apply (i : Fin n) : revOrderIso.symm i = OrderDual.toDual i.revPerm :=
   rfl
 #align fin.rev_order_iso_symm_apply Fin.revOrderIso_symm_apply
 -/
@@ -2508,7 +2508,7 @@ theorem sub_one_lt_iff {n : ℕ} {k : Fin (n + 1)} : k - 1 < k ↔ 0 < k :=
 -/
 
 #print Fin.last_sub /-
-theorem last_sub (i : Fin (n + 1)) : last n - i = i.rev :=
+theorem last_sub (i : Fin (n + 1)) : last n - i = i.revPerm :=
   ext <| by rw [coe_sub_iff_le.2 i.le_last, coe_last, coe_rev, Nat.succ_sub_succ_eq_sub]
 #align fin.last_sub Fin.last_sub
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

@@ -1324,89 +1324,91 @@ theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
 #align fin.cast_le_comp_cast_le Fin.castLE_comp_castLE
 -/
 
-#print Fin.cast /-
+#print Fin.castIso /-
 /-- `cast eq i` embeds `i` into a equal `fin` type, see also `equiv.fin_congr`. -/
-def cast (eq : n = m) : Fin n ≃o Fin m
+def castIso (eq : n = m) : Fin n ≃o Fin m
     where
   toEquiv := ⟨castLE Eq.le, castLE Eq.symm.le, fun a => eq_of_veq rfl, fun a => eq_of_veq rfl⟩
   map_rel_iff' a b := Iff.rfl
-#align fin.cast Fin.cast
+#align fin.cast Fin.castIso
 -/
 
-#print Fin.symm_cast /-
+#print Fin.symm_castIso /-
 @[simp]
-theorem symm_cast (h : n = m) : (cast h).symm = cast h.symm :=
+theorem symm_castIso (h : n = m) : (castIso h).symm = castIso h.symm :=
   rfl
-#align fin.symm_cast Fin.symm_cast
+#align fin.symm_cast Fin.symm_castIso
 -/
 
-#print Fin.coe_cast /-
+#print Fin.coe_castIso /-
 /-- While `fin.coe_order_iso_apply` is a more general case of this, we mark this `simp` anyway
 as it is eligible for `dsimp`. -/
 @[simp]
-theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : ℕ) = i :=
+theorem coe_castIso (h : n = m) (i : Fin n) : (castIso h i : ℕ) = i :=
   rfl
-#align fin.coe_cast Fin.coe_cast
+#align fin.coe_cast Fin.coe_castIso
 -/
 
-#print Fin.cast_zero /-
+#print Fin.castIso_zero /-
 @[simp]
-theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
-    cast h (0 : Fin n) =
+theorem castIso_zero {n' : ℕ} [NeZero n] {h : n = n'} :
+    castIso h (0 : Fin n) =
       haveI : NeZero n' := by rw [← h] <;> infer_instance
       0 :=
   ext rfl
-#align fin.cast_zero Fin.cast_zero
+#align fin.cast_zero Fin.castIso_zero
 -/
 
-#print Fin.cast_last /-
+#print Fin.castIso_last /-
 @[simp]
-theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
+theorem castIso_last {n' : ℕ} {h : n + 1 = n' + 1} : castIso h (last n) = last n' :=
   ext (by rw [coe_cast, coe_last, coe_last, Nat.succ_injective h])
-#align fin.cast_last Fin.cast_last
+#align fin.cast_last Fin.castIso_last
 -/
 
-#print Fin.cast_mk /-
+#print Fin.castIso_mk /-
 @[simp]
-theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h.le⟩ :=
+theorem castIso_mk (h : n = m) (i : ℕ) (hn : i < n) :
+    castIso h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h.le⟩ :=
   rfl
-#align fin.cast_mk Fin.cast_mk
+#align fin.cast_mk Fin.castIso_mk
 -/
 
-#print Fin.cast_trans /-
+#print Fin.castIso_trans /-
 @[simp]
-theorem cast_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
-    cast h' (cast h i) = cast (Eq.trans h h') i :=
+theorem castIso_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
+    castIso h' (castIso h i) = castIso (Eq.trans h h') i :=
   rfl
-#align fin.cast_trans Fin.cast_trans
+#align fin.cast_trans Fin.castIso_trans
 -/
 
-#print Fin.cast_refl /-
+#print Fin.castIso_refl /-
 @[simp]
-theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) := by ext; rfl
-#align fin.cast_refl Fin.cast_refl
+theorem castIso_refl (h : n = n := rfl) : castIso h = OrderIso.refl (Fin n) := by ext; rfl
+#align fin.cast_refl Fin.castIso_refl
 -/
 
 #print Fin.castLE_of_eq /-
 theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
-    (castLE h' : Fin m → Fin n) = Fin.cast h :=
+    (castLE h' : Fin m → Fin n) = Fin.castIso h :=
   funext fun _ => rfl
 #align fin.cast_le_of_eq Fin.castLE_of_eq
 -/
 
-#print Fin.cast_to_equiv /-
+#print Fin.castIso_to_equiv /-
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
-theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) := by subst h; simp
-#align fin.cast_to_equiv Fin.cast_to_equiv
+theorem castIso_to_equiv (h : n = m) : (castIso h).toEquiv = Equiv.cast (h ▸ rfl) := by subst h;
+  simp
+#align fin.cast_to_equiv Fin.castIso_to_equiv
 -/
 
-#print Fin.cast_eq_cast /-
+#print Fin.castIso_eq_cast /-
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
-theorem cast_eq_cast (h : n = m) : (cast h : Fin n → Fin m) = cast (h ▸ rfl) := by subst h; ext;
-  simp
-#align fin.cast_eq_cast Fin.cast_eq_cast
+theorem castIso_eq_cast (h : n = m) : (castIso h : Fin n → Fin m) = cast (h ▸ rfl) := by subst h;
+  ext; simp
+#align fin.cast_eq_cast Fin.castIso_eq_cast
 -/
 
 #print Fin.castAdd /-
@@ -1425,7 +1427,7 @@ theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
 
 #print Fin.castAdd_zero /-
 @[simp]
-theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = cast rfl :=
+theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = castIso rfl :=
   rfl
 #align fin.cast_add_zero Fin.castAdd_zero
 -/
@@ -1457,51 +1459,51 @@ theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt
 #align fin.cast_lt_cast_add Fin.castLT_castAdd
 -/
 
-#print Fin.castAdd_cast /-
+#print Fin.castAdd_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
-theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
-    castAdd m (Fin.cast h i) = Fin.cast (congr_arg _ h) (castAdd m i) :=
+theorem castAdd_castIso {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
+    castAdd m (Fin.castIso h i) = Fin.castIso (congr_arg _ h) (castAdd m i) :=
   ext rfl
-#align fin.cast_add_cast Fin.castAdd_cast
+#align fin.cast_add_cast Fin.castAdd_castIso
 -/
 
-#print Fin.cast_castAdd_left /-
-theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
-    cast h (castAdd m i) = castAdd m (cast (add_right_cancel h) i) :=
+#print Fin.castIso_castAdd_left /-
+theorem castIso_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
+    castIso h (castAdd m i) = castAdd m (castIso (add_right_cancel h) i) :=
   ext rfl
-#align fin.cast_cast_add_left Fin.cast_castAdd_left
+#align fin.cast_cast_add_left Fin.castIso_castAdd_left
 -/
 
-#print Fin.cast_castAdd_right /-
+#print Fin.castIso_castAdd_right /-
 @[simp]
-theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
-    cast h (castAdd m' i) = castAdd m i :=
+theorem castIso_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
+    castIso h (castAdd m' i) = castAdd m i :=
   ext rfl
-#align fin.cast_cast_add_right Fin.cast_castAdd_right
+#align fin.cast_cast_add_right Fin.castIso_castAdd_right
 -/
 
 #print Fin.castAdd_castAdd /-
 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
-    castAdd p (castAdd n i) = cast (add_assoc _ _ _).symm (castAdd (n + p) i) :=
+    castAdd p (castAdd n i) = castIso (add_assoc _ _ _).symm (castAdd (n + p) i) :=
   ext rfl
 #align fin.cast_add_cast_add Fin.castAdd_castAdd
 -/
 
-#print Fin.cast_succ_eq /-
+#print Fin.castIso_succ_eq /-
 /-- The cast of the successor is the succesor of the cast. See `fin.succ_cast_eq` for rewriting in
 the reverse direction. -/
 @[simp]
-theorem cast_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
-    cast h i.succ = (cast (Nat.succ.inj h) i).succ :=
+theorem castIso_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
+    castIso h i.succ = (castIso (Nat.succ.inj h) i).succ :=
   ext <| by simp
-#align fin.cast_succ_eq Fin.cast_succ_eq
+#align fin.cast_succ_eq Fin.castIso_succ_eq
 -/
 
-#print Fin.succ_cast_eq /-
-theorem succ_cast_eq {n' : ℕ} (i : Fin n) (h : n = n') :
-    (cast h i).succ = cast (by rw [h]) i.succ :=
+#print Fin.succ_castIso_eq /-
+theorem succ_castIso_eq {n' : ℕ} (i : Fin n) (h : n = n') :
+    (castIso h i).succ = castIso (by rw [h]) i.succ :=
   ext <| by simp
-#align fin.succ_cast_eq Fin.succ_cast_eq
+#align fin.succ_cast_eq Fin.succ_castIso_eq
 -/
 
 #print Fin.castSucc /-
@@ -1525,12 +1527,12 @@ theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt
 #align fin.cast_succ_mk Fin.castSucc_mk
 -/
 
-#print Fin.cast_castSucc /-
+#print Fin.castIso_castSucc /-
 @[simp]
-theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
-    cast h (castSucc i) = castSucc (cast (Nat.succ_injective h) i) := by ext;
+theorem castIso_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
+    castIso h (castSucc i) = castSucc (castIso (Nat.succ_injective h) i) := by ext;
   simp only [coe_cast, coe_cast_succ]
-#align fin.cast_cast_succ Fin.cast_castSucc
+#align fin.cast_cast_succ Fin.castIso_castSucc
 -/
 
 #print Fin.castSucc_lt_succ /-
@@ -1728,35 +1730,35 @@ theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, ad
 #align fin.add_nat_mk Fin.addNat_mk
 -/
 
-#print Fin.cast_addNat_zero /-
+#print Fin.castIso_addNat_zero /-
 @[simp]
-theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
-    cast h (addNat 0 i) = cast ((add_zero _).symm.trans h) i :=
+theorem castIso_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
+    castIso h (addNat 0 i) = castIso ((add_zero _).symm.trans h) i :=
   ext <| add_zero _
-#align fin.cast_add_nat_zero Fin.cast_addNat_zero
+#align fin.cast_add_nat_zero Fin.castIso_addNat_zero
 -/
 
-#print Fin.addNat_cast /-
+#print Fin.addNat_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
-theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
-    addNat m (cast h i) = cast (congr_arg _ h) (addNat m i) :=
+theorem addNat_castIso {n n' m : ℕ} (i : Fin n') (h : n' = n) :
+    addNat m (castIso h i) = castIso (congr_arg _ h) (addNat m i) :=
   ext rfl
-#align fin.add_nat_cast Fin.addNat_cast
+#align fin.add_nat_cast Fin.addNat_castIso
 -/
 
-#print Fin.cast_addNat_left /-
-theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
-    cast h (addNat m i) = addNat m (cast (add_right_cancel h) i) :=
+#print Fin.castIso_addNat_left /-
+theorem castIso_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
+    castIso h (addNat m i) = addNat m (castIso (add_right_cancel h) i) :=
   ext rfl
-#align fin.cast_add_nat_left Fin.cast_addNat_left
+#align fin.cast_add_nat_left Fin.castIso_addNat_left
 -/
 
-#print Fin.cast_addNat_right /-
+#print Fin.castIso_addNat_right /-
 @[simp]
-theorem cast_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
-    cast h (addNat m' i) = addNat m i :=
+theorem castIso_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
+    castIso h (addNat m' i) = addNat m i :=
   ext <| (congr_arg ((· + ·) (i : ℕ)) (add_left_cancel h) : _)
-#align fin.cast_add_nat_right Fin.cast_addNat_right
+#align fin.cast_add_nat_right Fin.castIso_addNat_right
 -/
 
 #print Fin.natAdd /-
@@ -1788,75 +1790,77 @@ theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAdd m i :=
 -/
 
 #print Fin.natAdd_zero /-
-theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRelEmbedding := by ext;
-  apply zero_add
+theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.castIso (zero_add n).symm).toRelEmbedding := by
+  ext; apply zero_add
 #align fin.nat_add_zero Fin.natAdd_zero
 -/
 
-#print Fin.natAdd_cast /-
+#print Fin.natAdd_castIso /-
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
-theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
-    natAdd m (cast h i) = cast (congr_arg _ h) (natAdd m i) :=
+theorem natAdd_castIso {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
+    natAdd m (castIso h i) = castIso (congr_arg _ h) (natAdd m i) :=
   ext rfl
-#align fin.nat_add_cast Fin.natAdd_cast
+#align fin.nat_add_cast Fin.natAdd_castIso
 -/
 
-#print Fin.cast_natAdd_right /-
-theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
-    cast h (natAdd m i) = natAdd m (cast (add_left_cancel h) i) :=
+#print Fin.castIso_natAdd_right /-
+theorem castIso_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
+    castIso h (natAdd m i) = natAdd m (castIso (add_left_cancel h) i) :=
   ext rfl
-#align fin.cast_nat_add_right Fin.cast_natAdd_right
+#align fin.cast_nat_add_right Fin.castIso_natAdd_right
 -/
 
-#print Fin.cast_natAdd_left /-
+#print Fin.castIso_natAdd_left /-
 @[simp]
-theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
-    cast h (natAdd m' i) = natAdd m i :=
+theorem castIso_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
+    castIso h (natAdd m' i) = natAdd m i :=
   ext <| (congr_arg (· + (i : ℕ)) (add_right_cancel h) : _)
-#align fin.cast_nat_add_left Fin.cast_natAdd_left
+#align fin.cast_nat_add_left Fin.castIso_natAdd_left
 -/
 
 #print Fin.castAdd_natAdd /-
 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
-    castAdd p (natAdd m i) = cast (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
+    castAdd p (natAdd m i) = castIso (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
   ext rfl
 #align fin.cast_add_nat_add Fin.castAdd_natAdd
 -/
 
 #print Fin.natAdd_castAdd /-
 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
-    natAdd m (castAdd p i) = cast (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
+    natAdd m (castAdd p i) = castIso (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
   ext rfl
 #align fin.nat_add_cast_add Fin.natAdd_castAdd
 -/
 
 #print Fin.natAdd_natAdd /-
 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
-    natAdd m (natAdd n i) = cast (add_assoc _ _ _) (natAdd (m + n) i) :=
+    natAdd m (natAdd n i) = castIso (add_assoc _ _ _) (natAdd (m + n) i) :=
   ext <| (add_assoc _ _ _).symm
 #align fin.nat_add_nat_add Fin.natAdd_natAdd
 -/
 
-#print Fin.cast_natAdd_zero /-
+#print Fin.castIso_natAdd_zero /-
 @[simp]
-theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
-    cast h (natAdd 0 i) = cast ((zero_add _).symm.trans h) i :=
+theorem castIso_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
+    castIso h (natAdd 0 i) = castIso ((zero_add _).symm.trans h) i :=
   ext <| zero_add _
-#align fin.cast_nat_add_zero Fin.cast_natAdd_zero
+#align fin.cast_nat_add_zero Fin.castIso_natAdd_zero
 -/
 
-#print Fin.cast_natAdd /-
+#print Fin.castIso_natAdd /-
 @[simp]
-theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAdd n i) = addNat n i :=
+theorem castIso_natAdd (n : ℕ) {m : ℕ} (i : Fin m) :
+    castIso (add_comm _ _) (natAdd n i) = addNat n i :=
   ext <| add_comm _ _
-#align fin.cast_nat_add Fin.cast_natAdd
+#align fin.cast_nat_add Fin.castIso_natAdd
 -/
 
-#print Fin.cast_addNat /-
+#print Fin.castIso_addNat /-
 @[simp]
-theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNat m i) = natAdd m i :=
+theorem castIso_addNat {n : ℕ} (m : ℕ) (i : Fin n) :
+    castIso (add_comm _ _) (addNat m i) = natAdd m i :=
   ext <| add_comm _ _
-#align fin.cast_add_nat Fin.cast_addNat
+#align fin.cast_add_nat Fin.castIso_addNat
 -/
 
 #print Fin.natAdd_last /-
@@ -2010,11 +2014,11 @@ theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addN
 #align fin.sub_nat_add_nat Fin.subNat_addNat
 -/
 
-#print Fin.natAdd_subNat_cast /-
+#print Fin.natAdd_subNat_castIso /-
 @[simp]
-theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
-    natAdd n (subNat n (cast (add_comm _ _) i) h) = i := by simp [← cast_add_nat]
-#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_cast
+theorem natAdd_subNat_castIso {i : Fin (n + m)} (h : n ≤ i) :
+    natAdd n (subNat n (castIso (add_comm _ _) i) h) = i := by simp [← cast_add_nat]
+#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castIso
 -/
 
 end Pred
@@ -2299,7 +2303,7 @@ theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fi
 def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd n i))
     (hright : ∀ i, C (natAdd m i)) (i : Fin (m + n)) : C i :=
   if hi : (i : ℕ) < m then Eq.recOn (castAdd_castLT n i hi) (hleft (castLT i hi))
-  else Eq.recOn (natAdd_subNat_cast (le_of_not_lt hi)) (hright _)
+  else Eq.recOn (natAdd_subNat_castIso (le_of_not_lt hi)) (hright _)
 #align fin.add_cases Fin.addCases
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -106,9 +106,11 @@ def elim0' {α : Sort _} (x : Fin 0) : α :=
 
 variable {n m : ℕ} {a b : Fin n}
 
+#print Fin.coeToNat /-
 instance coeToNat (n : ℕ) : Coe (Fin n) Nat :=
   ⟨Fin.val⟩
 #align fin.fin_to_nat Fin.coeToNat
+-/
 
 #print Fin.val_injective /-
 theorem val_injective : Function.Injective (@Fin.val n) :=
@@ -365,18 +367,24 @@ theorem mk_lt_mk {x y : Nat} {hx} {hy} : (⟨x, hx⟩ : Fin n) < ⟨y, hy⟩ ↔
 #align fin.mk_lt_mk Fin.mk_lt_mk
 -/
 
+#print Fin.min_val /-
 @[simp]
 theorem min_val : min (a : ℕ) n = a := by simp
 #align fin.min_coe Fin.min_val
+-/
 
+#print Fin.max_val /-
 @[simp]
 theorem max_val : max (a : ℕ) n = n := by simp
 #align fin.max_coe Fin.max_val
+-/
 
 instance {n : ℕ} : PartialOrder (Fin n) := by infer_instance
 
+#print Fin.val_strictMono /-
 theorem val_strictMono : StrictMono (coe : Fin n → ℕ) := fun _ _ => id
 #align fin.coe_strict_mono Fin.val_strictMono
+-/
 
 #print Fin.orderIsoSubtype /-
 /-- The equivalence `fin n ≃ { i // i < n }` is an order isomorphism. -/
@@ -443,53 +451,71 @@ instance hasOneOfNeZero [NeZero n] : One (Fin n) :=
   ⟨ofNat'' 1⟩
 #align fin.has_one_of_ne_zero Fin.hasOneOfNeZero
 
+#print Fin.val_zero /-
 @[simp]
 theorem val_zero (n : ℕ) [NeZero n] : ((0 : Fin n) : ℕ) = 0 :=
   rfl
 #align fin.coe_zero Fin.val_zero
+-/
 
 attribute [simp] val_zero
 
 /- warning: fin.val_zero' clashes with fin.coe_zero -> Fin.val_zero
 Case conversion may be inaccurate. Consider using '#align fin.val_zero' Fin.val_zeroₓ'. -/
+#print Fin.val_zero /-
 @[simp]
 theorem val_zero (n) [NeZero n] : (0 : Fin n).val = 0 :=
   rfl
 #align fin.val_zero' Fin.val_zero
+-/
 
+#print Fin.mk_zero /-
 @[simp]
 theorem mk_zero [NeZero n] : (⟨0, Nat.pos_of_ne_zero (NeZero.ne n)⟩ : Fin n) = (0 : Fin _) :=
   rfl
 #align fin.mk_zero Fin.mk_zero
+-/
 
+#print Fin.zero_le /-
 @[simp]
 theorem zero_le [NeZero n] (a : Fin n) : 0 ≤ a :=
   zero_le a.1
 #align fin.zero_le Fin.zero_le
+-/
 
+#print Fin.zero_lt_one /-
 theorem zero_lt_one : (0 : Fin (n + 2)) < 1 :=
   Nat.zero_lt_one
 #align fin.zero_lt_one Fin.zero_lt_one
+-/
 
+#print Fin.not_lt_zero /-
 @[simp]
 theorem not_lt_zero (a : Fin n.succ) : ¬a < 0 :=
   fun.
 #align fin.not_lt_zero Fin.not_lt_zero
+-/
 
+#print Fin.pos_iff_ne_zero /-
 theorem pos_iff_ne_zero [NeZero n] (a : Fin n) : 0 < a ↔ a ≠ 0 := by
   rw [← coe_fin_lt, coe_zero, pos_iff_ne_zero, Ne.def, Ne.def, ext_iff, coe_zero]
 #align fin.pos_iff_ne_zero Fin.pos_iff_ne_zero
+-/
 
+#print Fin.eq_zero_or_eq_succ /-
 theorem eq_zero_or_eq_succ {n : ℕ} (i : Fin (n + 1)) : i = 0 ∨ ∃ j : Fin n, i = j.succ :=
   by
   rcases i with ⟨_ | j, h⟩
   · left; rfl
   · right; exact ⟨⟨j, Nat.lt_of_succ_lt_succ h⟩, rfl⟩
 #align fin.eq_zero_or_eq_succ Fin.eq_zero_or_eq_succ
+-/
 
+#print Fin.eq_succ_of_ne_zero /-
 theorem eq_succ_of_ne_zero {n : ℕ} {i : Fin (n + 1)} (hi : i ≠ 0) : ∃ j : Fin n, i = j.succ :=
   (eq_zero_or_eq_succ i).resolve_left hi
 #align fin.eq_succ_of_ne_zero Fin.eq_succ_of_ne_zero
+-/
 
 #print Fin.rev /-
 /-- The antitone involution `fin n → fin n` given by `i ↦ n-(i+1)`. -/
@@ -501,10 +527,12 @@ def rev : Equiv.Perm (Fin n) :=
 #align fin.rev Fin.rev
 -/
 
+#print Fin.val_rev /-
 @[simp]
 theorem val_rev (i : Fin n) : (i.rev : ℕ) = n - (i + 1) :=
   rfl
 #align fin.coe_rev Fin.val_rev
+-/
 
 #print Fin.rev_involutive /-
 theorem rev_involutive : Involutive (@rev n) :=
@@ -587,10 +615,12 @@ def revOrderIso {n} : (Fin n)ᵒᵈ ≃o Fin n :=
 #align fin.rev_order_iso Fin.revOrderIso
 -/
 
+#print Fin.revOrderIso_symm_apply /-
 @[simp]
 theorem revOrderIso_symm_apply (i : Fin n) : revOrderIso.symm i = OrderDual.toDual i.rev :=
   rfl
 #align fin.rev_order_iso_symm_apply Fin.revOrderIso_symm_apply
+-/
 
 #print Fin.last /-
 /-- The greatest value of `fin (n+1)` -/
@@ -629,8 +659,10 @@ instance : BoundedOrder (Fin (n + 1)) where
 instance : Lattice (Fin (n + 1)) :=
   LinearOrder.toLattice
 
+#print Fin.last_pos /-
 theorem last_pos : (0 : Fin (n + 2)) < last (n + 1) := by simp [lt_iff_coe_lt_coe]
 #align fin.last_pos Fin.last_pos
+-/
 
 #print Fin.eq_last_of_not_lt /-
 theorem eq_last_of_not_lt {i : Fin (n + 1)} (h : ¬(i : ℕ) < n) : i = last n :=
@@ -638,13 +670,17 @@ theorem eq_last_of_not_lt {i : Fin (n + 1)} (h : ¬(i : ℕ) < n) : i = last n :
 #align fin.eq_last_of_not_lt Fin.eq_last_of_not_lt
 -/
 
+#print Fin.top_eq_last /-
 theorem top_eq_last (n : ℕ) : ⊤ = Fin.last n :=
   rfl
 #align fin.top_eq_last Fin.top_eq_last
+-/
 
+#print Fin.bot_eq_zero /-
 theorem bot_eq_zero (n : ℕ) : ⊥ = (0 : Fin (n + 1)) :=
   rfl
 #align fin.bot_eq_zero Fin.bot_eq_zero
+-/
 
 section
 
@@ -652,6 +688,7 @@ variable {α : Type _} [Preorder α]
 
 open Set
 
+#print Fin.coe_orderIso_apply /-
 /-- If `e` is an `order_iso` between `fin n` and `fin m`, then `n = m` and `e` is the identity
 map. In this lemma we state that for each `i : fin n` we have `(e i : ℕ) = (i : ℕ)`. -/
 @[simp]
@@ -667,6 +704,7 @@ theorem coe_orderIso_apply (e : Fin n ≃o Fin m) (i : Fin n) : (e i : ℕ) = i
     simpa using h _ this (e.symm _).is_lt
   · rwa [← h j hj (hj.trans hi), ← lt_iff_coe_lt_coe, e.lt_iff_lt]
 #align fin.coe_order_iso_apply Fin.coe_orderIso_apply
+-/
 
 #print Fin.orderIso_subsingleton /-
 instance orderIso_subsingleton : Subsingleton (Fin n ≃o α) :=
@@ -689,6 +727,7 @@ instance orderIsoUnique : Unique (Fin n ≃o Fin n) :=
 #align fin.order_iso_unique Fin.orderIsoUnique
 -/
 
+#print Fin.strictMono_unique /-
 /-- Two strictly monotone functions from `fin n` are equal provided that their ranges
 are equal. -/
 theorem strictMono_unique {f g : Fin n → α} (hf : StrictMono f) (hg : StrictMono g)
@@ -696,11 +735,14 @@ theorem strictMono_unique {f g : Fin n → α} (hf : StrictMono f) (hg : StrictM
   have : (hf.OrderIso f).trans (OrderIso.setCongr _ _ h) = hg.OrderIso g := Subsingleton.elim _ _
   congr_arg (Function.comp (coe : range g → α)) (funext <| RelIso.ext_iff.1 this)
 #align fin.strict_mono_unique Fin.strictMono_unique
+-/
 
+#print Fin.orderEmbedding_eq /-
 /-- Two order embeddings of `fin n` are equal provided that their ranges are equal. -/
 theorem orderEmbedding_eq {f g : Fin n ↪o α} (h : range f = range g) : f = g :=
   RelEmbedding.ext <| funext_iff.1 <| strictMono_unique f.StrictMono g.StrictMono h
 #align fin.order_embedding_eq Fin.orderEmbedding_eq
+-/
 
 end
 
@@ -765,15 +807,19 @@ theorem subsingleton_iff_le_one : Subsingleton (Fin n) ↔ n ≤ 1 := by
 
 section Monoid
 
+#print Fin.add_zero /-
 @[simp]
 protected theorem add_zero [NeZero n] (k : Fin n) : k + 0 = k := by
   simp [eq_iff_veq, add_def, mod_eq_of_lt (is_lt k)]
 #align fin.add_zero Fin.add_zero
+-/
 
+#print Fin.zero_add /-
 @[simp]
 protected theorem zero_add [NeZero n] (k : Fin n) : (0 : Fin n) + k = k := by
   simp [eq_iff_veq, add_def, mod_eq_of_lt (is_lt k)]
 #align fin.zero_add Fin.zero_add
+-/
 
 #print Fin.addCommMonoid /-
 instance addCommMonoid (n : ℕ) [NeZero n] : AddCommMonoid (Fin n)
@@ -810,11 +856,13 @@ theorem val_add {n : ℕ} : ∀ a b : Fin n, ((a + b : Fin n) : ℕ) = (a + b) %
 #align fin.coe_add Fin.val_add
 -/
 
+#print Fin.val_add_eq_ite /-
 theorem val_add_eq_ite {n : ℕ} (a b : Fin n) :
     (↑(a + b) : ℕ) = if n ≤ a + b then a + b - n else a + b := by
   rw [Fin.val_add, Nat.add_mod_eq_ite, Nat.mod_eq_of_lt (show ↑a < n from a.2),
     Nat.mod_eq_of_lt (show ↑b < n from b.2)]
 #align fin.coe_add_eq_ite Fin.val_add_eq_ite
+-/
 
 #print Fin.val_bit0 /-
 theorem val_bit0 {n : ℕ} (k : Fin n) : ((bit0 k : Fin n) : ℕ) = bit0 (k : ℕ) % n := by cases k; rfl
@@ -839,12 +887,15 @@ theorem val_add_one_of_lt {n : ℕ} {i : Fin n.succ} (h : i < last _) : (↑(i +
 #align fin.coe_add_one_of_lt Fin.val_add_one_of_lt
 -/
 
+#print Fin.last_add_one /-
 @[simp]
 theorem last_add_one : ∀ n, last n + 1 = 0
   | 0 => Subsingleton.elim _ _
   | n + 1 => by ext; rw [coe_add, coe_zero, coe_last, coe_one, Nat.mod_self]
 #align fin.last_add_one Fin.last_add_one
+-/
 
+#print Fin.val_add_one /-
 theorem val_add_one {n : ℕ} (i : Fin (n + 1)) :
     ((i + 1 : Fin (n + 1)) : ℕ) = if i = last _ then 0 else i + 1 :=
   by
@@ -852,6 +903,7 @@ theorem val_add_one {n : ℕ} (i : Fin (n + 1)) :
   · simp
   · simpa [h.ne] using coe_add_one_of_lt h
 #align fin.coe_add_one Fin.val_add_one
+-/
 
 section Bit
 
@@ -895,16 +947,19 @@ theorem val_two {n : ℕ} : ((2 : Fin (n + 3)) : ℕ) = 2 :=
 
 section OfNatCoe
 
+#print Fin.ofNat_eq_val /-
 @[simp]
 theorem ofNat_eq_val (n : ℕ) (a : ℕ) : (ofNat a : Fin (n + 1)) = a :=
   rfl
 #align fin.of_nat_eq_coe Fin.ofNat_eq_val
+-/
 
 @[simp]
 theorem ofNat''_eq_coe (n : ℕ) [NeZero n] (a : ℕ) : (ofNat'' a : Fin n) = a :=
   rfl
 #align fin.of_nat'_eq_coe Fin.ofNat''ₓ_eq_coe
 
+#print Fin.val_cast_of_lt /-
 /-- Converting an in-range number to `fin n` produces a result
 whose value is the original number.  -/
 theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : (a : Fin n).val = a :=
@@ -912,7 +967,9 @@ theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : (a : Fin n).
   rw [← of_nat'_eq_coe]
   exact Nat.mod_eq_of_lt h
 #align fin.coe_val_of_lt Fin.val_cast_of_lt
+-/
 
+#print Fin.cast_val_eq_self /-
 /-- Converting the value of a `fin n` to `fin n` results
 in the same value.  -/
 theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a :=
@@ -920,33 +977,43 @@ theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a
   rw [Fin.eq_iff_veq]
   exact coe_val_of_lt a.property
 #align fin.coe_val_eq_self Fin.cast_val_eq_self
+-/
 
 /- warning: fin.coe_coe_of_lt clashes with fin.coe_val_of_lt -> Fin.val_cast_of_lt
 Case conversion may be inaccurate. Consider using '#align fin.coe_coe_of_lt Fin.val_cast_of_ltₓ'. -/
+#print Fin.val_cast_of_lt /-
 /-- Coercing an in-range number to `fin n`, and converting back
 to `ℕ`, results in that number. -/
 theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : ((a : Fin n) : ℕ) = a :=
   val_cast_of_lt h
 #align fin.coe_coe_of_lt Fin.val_cast_of_lt
+-/
 
 /- warning: fin.coe_coe_eq_self clashes with fin.coe_val_eq_self -> Fin.cast_val_eq_self
 Case conversion may be inaccurate. Consider using '#align fin.coe_coe_eq_self Fin.cast_val_eq_selfₓ'. -/
+#print Fin.cast_val_eq_self /-
 /-- Converting a `fin n` to `ℕ` and back results in the same
 value. -/
 @[simp]
 theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : ((a : ℕ) : Fin n) = a :=
   cast_val_eq_self a
 #align fin.coe_coe_eq_self Fin.cast_val_eq_self
+-/
 
+#print Fin.cast_nat_eq_last /-
 theorem cast_nat_eq_last (n) : (n : Fin (n + 1)) = Fin.last n := by
   rw [← Fin.ofNat_eq_val, Fin.ofNat, Fin.last]; simp only [Nat.mod_eq_of_lt n.lt_succ_self]
 #align fin.coe_nat_eq_last Fin.cast_nat_eq_last
+-/
 
+#print Fin.le_val_last /-
 theorem le_val_last (i : Fin (n + 1)) : i ≤ n := by rw [Fin.cast_nat_eq_last]; exact Fin.le_last i
 #align fin.le_coe_last Fin.le_val_last
+-/
 
 end OfNatCoe
 
+#print Fin.add_one_pos /-
 theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) < i + 1 :=
   by
   cases n
@@ -955,15 +1022,21 @@ theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) <
     rw [lt_iff_coe_lt_coe, coe_add, coe_zero, coe_one, Nat.mod_eq_of_lt h]
     exact Nat.zero_lt_succ _
 #align fin.add_one_pos Fin.add_one_pos
+-/
 
+#print Fin.one_pos /-
 theorem one_pos : (0 : Fin (n + 2)) < 1 :=
   succ_pos 0
 #align fin.one_pos Fin.one_pos
+-/
 
+#print Fin.zero_ne_one /-
 theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 :=
   ne_of_lt one_pos
 #align fin.zero_ne_one Fin.zero_ne_one
+-/
 
+#print Fin.zero_eq_one_iff /-
 @[simp]
 theorem zero_eq_one_iff [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 :=
   by
@@ -974,10 +1047,13 @@ theorem zero_eq_one_iff [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 :=
     exact eq_one_of_dvd_one this
   · rintro rfl; rfl
 #align fin.zero_eq_one_iff Fin.zero_eq_one_iff
+-/
 
+#print Fin.one_eq_zero_iff /-
 @[simp]
 theorem one_eq_zero_iff [NeZero n] : (1 : Fin n) = 0 ↔ n = 1 := by rw [eq_comm, zero_eq_one_iff]
 #align fin.one_eq_zero_iff Fin.one_eq_zero_iff
+-/
 
 end Add
 
@@ -994,19 +1070,25 @@ theorem val_succ (j : Fin n) : (j.succ : ℕ) = j + 1 := by cases j <;> simp [Fi
 #align fin.coe_succ Fin.val_succ
 -/
 
+#print Fin.succ_pos /-
 @[simp]
 theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by simp [lt_iff_coe_lt_coe]
 #align fin.succ_pos Fin.succ_pos
+-/
 
+#print Fin.succEmbedding /-
 /-- `fin.succ` as an `order_embedding` -/
 def succEmbedding (n : ℕ) : Fin n ↪o Fin (n + 1) :=
   OrderEmbedding.ofStrictMono Fin.succ fun ⟨i, hi⟩ ⟨j, hj⟩ h => succ_lt_succ h
 #align fin.succ_embedding Fin.succEmbedding
+-/
 
+#print Fin.val_succEmbedding /-
 @[simp]
 theorem val_succEmbedding : ⇑(succEmbedding n) = Fin.succ :=
   rfl
 #align fin.coe_succ_embedding Fin.val_succEmbedding
+-/
 
 #print Fin.succ_le_succ_iff /-
 @[simp]
@@ -1035,10 +1117,13 @@ theorem succ_inj {a b : Fin n} : a.succ = b.succ ↔ a = b :=
 #align fin.succ_inj Fin.succ_inj
 -/
 
+#print Fin.succ_ne_zero /-
 theorem succ_ne_zero {n} : ∀ k : Fin n, Fin.succ k ≠ 0
   | ⟨k, hk⟩, HEq => Nat.succ_ne_zero k <| ext_iff.1 HEq
 #align fin.succ_ne_zero Fin.succ_ne_zero
+-/
 
+#print Fin.succ_zero_eq_one /-
 @[simp]
 theorem succ_zero_eq_one [NeZero n] : Fin.succ (0 : Fin n) = 1 :=
   by
@@ -1046,12 +1131,15 @@ theorem succ_zero_eq_one [NeZero n] : Fin.succ (0 : Fin n) = 1 :=
   · exact (NeZero.ne 0 rfl).elim
   · rfl
 #align fin.succ_zero_eq_one Fin.succ_zero_eq_one
+-/
 
+#print Fin.succ_zero_eq_one' /-
 /-- Version of `succ_zero_eq_one` to be used by `dsimp` -/
 @[simp]
 theorem succ_zero_eq_one' : Fin.succ (0 : Fin (n + 1)) = 1 :=
   rfl
 #align fin.succ_zero_eq_one' Fin.succ_zero_eq_one'
+-/
 
 #print Fin.succ_one_eq_two /-
 @[simp]
@@ -1078,9 +1166,11 @@ theorem succ_mk (n i : ℕ) (h : i < n) : Fin.succ ⟨i, h⟩ = ⟨i + 1, Nat.su
 #align fin.succ_mk Fin.succ_mk
 -/
 
+#print Fin.mk_succ_pos /-
 theorem mk_succ_pos (i : ℕ) (h : i < n) : (0 : Fin (n + 1)) < ⟨i.succ, add_lt_add_right h 1⟩ := by
   rw [lt_iff_coe_lt_coe, coe_zero]; exact Nat.succ_pos i
 #align fin.mk_succ_pos Fin.mk_succ_pos
+-/
 
 #print Fin.one_lt_succ_succ /-
 theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ :=
@@ -1132,10 +1222,12 @@ theorem lt_add_one_iff {n : ℕ} {k : Fin (n + 1)} : k < k + 1 ↔ k < last n :=
 #align fin.lt_add_one_iff Fin.lt_add_one_iff
 -/
 
+#print Fin.le_zero_iff /-
 @[simp]
 theorem le_zero_iff {n : ℕ} [NeZero n] {k : Fin n} : k ≤ 0 ↔ k = 0 :=
   ⟨fun h => Fin.eq_of_veq <| by rw [Nat.eq_zero_of_le_zero h] <;> rfl, by rintro rfl <;> rfl⟩
 #align fin.le_zero_iff Fin.le_zero_iff
+-/
 
 #print Fin.succ_succ_ne_one /-
 theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
@@ -1171,26 +1263,35 @@ def castLE (h : n ≤ m) : Fin n ↪o Fin m :=
 #align fin.cast_le Fin.castLE
 -/
 
+#print Fin.coe_castLE /-
 @[simp]
 theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
   rfl
 #align fin.coe_cast_le Fin.coe_castLE
+-/
 
+#print Fin.castLE_mk /-
 @[simp]
 theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
     castLE h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h⟩ :=
   rfl
 #align fin.cast_le_mk Fin.castLE_mk
+-/
 
+#print Fin.castLE_zero /-
 @[simp]
 theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [eq_iff_veq]
 #align fin.cast_le_zero Fin.castLE_zero
+-/
 
+#print Fin.range_castLE /-
 @[simp]
 theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = {i | (i : ℕ) < n} :=
   Set.ext fun x => ⟨fun ⟨y, hy⟩ => hy ▸ y.2, fun hx => ⟨⟨x, hx⟩, Fin.ext rfl⟩⟩
 #align fin.range_cast_le Fin.range_castLE
+-/
 
+#print Fin.coe_of_injective_castLE_symm /-
 @[simp]
 theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
     ((Equiv.ofInjective _ (castLE h).Injective).symm ⟨i, hi⟩ : ℕ) = i :=
@@ -1198,23 +1299,30 @@ theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi)
   rw [← coe_cast_le]
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
 #align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symm
+-/
 
+#print Fin.castLE_succ /-
 @[simp]
 theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
     castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.eq_iff_veq]
 #align fin.cast_le_succ Fin.castLE_succ
+-/
 
+#print Fin.castLE_castLE /-
 @[simp]
 theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
     Fin.castLE mn (Fin.castLE km i) = Fin.castLE (km.trans mn) i :=
   Fin.ext (by simp only [coe_cast_le])
 #align fin.cast_le_cast_le Fin.castLE_castLE
+-/
 
+#print Fin.castLE_comp_castLE /-
 @[simp]
 theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
     Fin.castLE mn ∘ Fin.castLE km = Fin.castLE (km.trans mn) :=
   funext (castLE_castLE km mn)
 #align fin.cast_le_comp_cast_le Fin.castLE_comp_castLE
+-/
 
 #print Fin.cast /-
 /-- `cast eq i` embeds `i` into a equal `fin` type, see also `equiv.fin_congr`. -/
@@ -1232,13 +1340,16 @@ theorem symm_cast (h : n = m) : (cast h).symm = cast h.symm :=
 #align fin.symm_cast Fin.symm_cast
 -/
 
+#print Fin.coe_cast /-
 /-- While `fin.coe_order_iso_apply` is a more general case of this, we mark this `simp` anyway
 as it is eligible for `dsimp`. -/
 @[simp]
 theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : ℕ) = i :=
   rfl
 #align fin.coe_cast Fin.coe_cast
+-/
 
+#print Fin.cast_zero /-
 @[simp]
 theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
     cast h (0 : Fin n) =
@@ -1246,22 +1357,29 @@ theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
       0 :=
   ext rfl
 #align fin.cast_zero Fin.cast_zero
+-/
 
+#print Fin.cast_last /-
 @[simp]
 theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
   ext (by rw [coe_cast, coe_last, coe_last, Nat.succ_injective h])
 #align fin.cast_last Fin.cast_last
+-/
 
+#print Fin.cast_mk /-
 @[simp]
 theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h.le⟩ :=
   rfl
 #align fin.cast_mk Fin.cast_mk
+-/
 
+#print Fin.cast_trans /-
 @[simp]
 theorem cast_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
     cast h' (cast h i) = cast (Eq.trans h h') i :=
   rfl
 #align fin.cast_trans Fin.cast_trans
+-/
 
 #print Fin.cast_refl /-
 @[simp]
@@ -1269,10 +1387,12 @@ theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) := by ext;
 #align fin.cast_refl Fin.cast_refl
 -/
 
+#print Fin.castLE_of_eq /-
 theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
     (castLE h' : Fin m → Fin n) = Fin.cast h :=
   funext fun _ => rfl
 #align fin.cast_le_of_eq Fin.castLE_of_eq
+-/
 
 #print Fin.cast_to_equiv /-
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
@@ -1281,11 +1401,13 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 #align fin.cast_to_equiv Fin.cast_to_equiv
 -/
 
+#print Fin.cast_eq_cast /-
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
 theorem cast_eq_cast (h : n = m) : (cast h : Fin n → Fin m) = cast (h ▸ rfl) := by subst h; ext;
   simp
 #align fin.cast_eq_cast Fin.cast_eq_cast
+-/
 
 #print Fin.castAdd /-
 /-- `cast_add m i` embeds `i : fin n` in `fin (n+m)`. See also `fin.nat_add` and `fin.add_nat`. -/
@@ -1294,57 +1416,78 @@ def castAdd (m) : Fin n ↪o Fin (n + m) :=
 #align fin.cast_add Fin.castAdd
 -/
 
+#print Fin.coe_castAdd /-
 @[simp]
 theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
   rfl
 #align fin.coe_cast_add Fin.coe_castAdd
+-/
 
+#print Fin.castAdd_zero /-
 @[simp]
 theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = cast rfl :=
   rfl
 #align fin.cast_add_zero Fin.castAdd_zero
+-/
 
+#print Fin.castAdd_lt /-
 theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAdd n i : ℕ) < m :=
   i.2
 #align fin.cast_add_lt Fin.castAdd_lt
+-/
 
+#print Fin.castAdd_mk /-
 @[simp]
 theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i, lt_add_right i n m h⟩ :=
   rfl
 #align fin.cast_add_mk Fin.castAdd_mk
+-/
 
+#print Fin.castAdd_castLT /-
 @[simp]
 theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m (castLT i hi) = i :=
   ext rfl
 #align fin.cast_add_cast_lt Fin.castAdd_castLT
+-/
 
+#print Fin.castLT_castAdd /-
 @[simp]
 theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt m i) = i :=
   ext rfl
 #align fin.cast_lt_cast_add Fin.castLT_castAdd
+-/
 
+#print Fin.castAdd_cast /-
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
     castAdd m (Fin.cast h i) = Fin.cast (congr_arg _ h) (castAdd m i) :=
   ext rfl
 #align fin.cast_add_cast Fin.castAdd_cast
+-/
 
+#print Fin.cast_castAdd_left /-
 theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (castAdd m i) = castAdd m (cast (add_right_cancel h) i) :=
   ext rfl
 #align fin.cast_cast_add_left Fin.cast_castAdd_left
+-/
 
+#print Fin.cast_castAdd_right /-
 @[simp]
 theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
     cast h (castAdd m' i) = castAdd m i :=
   ext rfl
 #align fin.cast_cast_add_right Fin.cast_castAdd_right
+-/
 
+#print Fin.castAdd_castAdd /-
 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
     castAdd p (castAdd n i) = cast (add_assoc _ _ _).symm (castAdd (n + p) i) :=
   ext rfl
 #align fin.cast_add_cast_add Fin.castAdd_castAdd
+-/
 
+#print Fin.cast_succ_eq /-
 /-- The cast of the successor is the succesor of the cast. See `fin.succ_cast_eq` for rewriting in
 the reverse direction. -/
 @[simp]
@@ -1352,11 +1495,14 @@ theorem cast_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
     cast h i.succ = (cast (Nat.succ.inj h) i).succ :=
   ext <| by simp
 #align fin.cast_succ_eq Fin.cast_succ_eq
+-/
 
+#print Fin.succ_cast_eq /-
 theorem succ_cast_eq {n' : ℕ} (i : Fin n) (h : n = n') :
     (cast h i).succ = cast (by rw [h]) i.succ :=
   ext <| by simp
 #align fin.succ_cast_eq Fin.succ_cast_eq
+-/
 
 #print Fin.castSucc /-
 /-- `cast_succ i` embeds `i : fin n` in `fin (n+1)`. -/
@@ -1365,35 +1511,47 @@ def castSucc : Fin n ↪o Fin (n + 1) :=
 #align fin.cast_succ Fin.castSucc
 -/
 
+#print Fin.coe_castSucc /-
 @[simp]
 theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
   rfl
 #align fin.coe_cast_succ Fin.coe_castSucc
+-/
 
+#print Fin.castSucc_mk /-
 @[simp]
 theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
   rfl
 #align fin.cast_succ_mk Fin.castSucc_mk
+-/
 
+#print Fin.cast_castSucc /-
 @[simp]
 theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
     cast h (castSucc i) = castSucc (cast (Nat.succ_injective h) i) := by ext;
   simp only [coe_cast, coe_cast_succ]
 #align fin.cast_cast_succ Fin.cast_castSucc
+-/
 
+#print Fin.castSucc_lt_succ /-
 theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
   lt_iff_val_lt_val.2 <| by simp only [coe_cast_succ, coe_succ, Nat.lt_succ_self]
 #align fin.cast_succ_lt_succ Fin.castSucc_lt_succ
+-/
 
+#print Fin.le_castSucc_iff /-
 theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
   simpa [lt_iff_coe_lt_coe, le_iff_coe_le_coe] using nat.succ_le_succ_iff.symm
 #align fin.le_cast_succ_iff Fin.le_castSucc_iff
+-/
 
+#print Fin.castSucc_lt_iff_succ_le /-
 theorem castSucc_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
     i.cast_succ < j ↔ i.succ ≤ j := by
   simpa only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc] using
     Nat.lt_iff_add_one_le
 #align fin.cast_succ_lt_iff_succ_le Fin.castSucc_lt_iff_succ_le
+-/
 
 #print Fin.succ_last /-
 @[simp]
@@ -1409,68 +1567,95 @@ theorem succ_eq_last_succ {n : ℕ} (i : Fin n.succ) : i.succ = last (n + 1) ↔
 #align fin.succ_eq_last_succ Fin.succ_eq_last_succ
 -/
 
+#print Fin.castSucc_castLT /-
 @[simp]
 theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT i h) = i :=
   Fin.eq_of_veq rfl
 #align fin.cast_succ_cast_lt Fin.castSucc_castLT
+-/
 
+#print Fin.castLT_castSucc /-
 @[simp]
 theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSucc a) h = a := by
   cases a <;> rfl
 #align fin.cast_lt_cast_succ Fin.castLT_castSucc
+-/
 
+#print Fin.castSucc_lt_castSucc_iff /-
 @[simp]
 theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
   (@castSucc n).lt_iff_lt
 #align fin.cast_succ_lt_cast_succ_iff Fin.castSucc_lt_castSucc_iff
+-/
 
+#print Fin.castSucc_injective /-
 theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
   (castSucc : Fin n ↪o _).Injective
 #align fin.cast_succ_injective Fin.castSucc_injective
+-/
 
+#print Fin.castSucc_inj /-
 theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
   (castSucc_injective n).eq_iff
 #align fin.cast_succ_inj Fin.castSucc_inj
+-/
 
+#print Fin.castSucc_lt_last /-
 theorem castSucc_lt_last (a : Fin n) : castSucc a < last n :=
   lt_iff_val_lt_val.mpr a.is_lt
 #align fin.cast_succ_lt_last Fin.castSucc_lt_last
+-/
 
+#print Fin.castSucc_zero /-
 @[simp]
 theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
   rfl
 #align fin.cast_succ_zero Fin.castSucc_zero
+-/
 
+#print Fin.castSucc_one /-
 @[simp]
 theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
   rfl
 #align fin.cast_succ_one Fin.castSucc_one
+-/
 
+#print Fin.castSucc_pos /-
 /-- `cast_succ i` is positive when `i` is positive -/
 theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
   simpa [lt_iff_coe_lt_coe] using h
 #align fin.cast_succ_pos Fin.castSucc_pos
+-/
 
+#print Fin.castSucc_eq_zero_iff /-
 @[simp]
 theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
   Fin.ext_iff.trans <| (Fin.ext_iff.trans <| Iff.rfl).symm
 #align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iff
+-/
 
+#print Fin.castSucc_ne_zero_iff /-
 theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
   not_iff_not.mpr <| castSucc_eq_zero_iff a
 #align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iff
+-/
 
+#print Fin.castSucc_fin_succ /-
 theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.succ (castSucc j) := by
   simp [Fin.ext_iff]
 #align fin.cast_succ_fin_succ Fin.castSucc_fin_succ
+-/
 
+#print Fin.coe_eq_castSucc /-
 @[norm_cast, simp]
 theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
   by
   ext
   exact coe_val_of_lt (Nat.lt.step a.is_lt)
 #align fin.coe_eq_cast_succ Fin.coe_eq_castSucc
+-/
 
+#print Fin.coeSucc_eq_succ /-
 @[simp]
 theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
   by
@@ -1478,16 +1663,22 @@ theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
   · exact finZeroElim a
   · simp [a.is_lt, eq_iff_veq, add_def, Nat.mod_eq_of_lt]
 #align fin.coe_succ_eq_succ Fin.coeSucc_eq_succ
+-/
 
+#print Fin.lt_succ /-
 theorem lt_succ : a.cast_succ < a.succ := by
   rw [cast_succ, lt_iff_coe_lt_coe, coe_cast_add, coe_succ]; exact lt_add_one a.val
 #align fin.lt_succ Fin.lt_succ
+-/
 
+#print Fin.range_castSucc /-
 @[simp]
 theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = {i | (i : ℕ) < n} :=
   range_castLE _
 #align fin.range_cast_succ Fin.range_castSucc
+-/
 
+#print Fin.coe_of_injective_castSucc_symm /-
 @[simp]
 theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
     ((Equiv.ofInjective castSucc (castSucc_injective _)).symm ⟨i, hi⟩ : ℕ) = i :=
@@ -1495,10 +1686,13 @@ theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
   rw [← coe_cast_succ]
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
 #align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symm
+-/
 
+#print Fin.succ_castSucc /-
 theorem succ_castSucc {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
   Fin.ext (by simp)
 #align fin.succ_cast_succ Fin.succ_castSucc
+-/
 
 #print Fin.addNat /-
 /-- `add_nat m i` adds `m` to `i`, generalizes `fin.succ`. -/
@@ -1508,46 +1702,62 @@ def addNat (m) : Fin n ↪o Fin (n + m) :=
 #align fin.add_nat Fin.addNat
 -/
 
+#print Fin.coe_addNat /-
 @[simp]
 theorem coe_addNat (m : ℕ) (i : Fin n) : (addNat m i : ℕ) = i + m :=
   rfl
 #align fin.coe_add_nat Fin.coe_addNat
+-/
 
+#print Fin.addNat_one /-
 @[simp]
 theorem addNat_one {i : Fin n} : addNat 1 i = i.succ := by ext; rw [coe_add_nat, coe_succ]
 #align fin.add_nat_one Fin.addNat_one
+-/
 
+#print Fin.le_coe_addNat /-
 theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNat m i :=
   Nat.le_add_left _ _
 #align fin.le_coe_add_nat Fin.le_coe_addNat
+-/
 
+#print Fin.addNat_mk /-
 @[simp]
 theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, add_lt_add_right hi n⟩ :=
   rfl
 #align fin.add_nat_mk Fin.addNat_mk
+-/
 
+#print Fin.cast_addNat_zero /-
 @[simp]
 theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
     cast h (addNat 0 i) = cast ((add_zero _).symm.trans h) i :=
   ext <| add_zero _
 #align fin.cast_add_nat_zero Fin.cast_addNat_zero
+-/
 
+#print Fin.addNat_cast /-
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
     addNat m (cast h i) = cast (congr_arg _ h) (addNat m i) :=
   ext rfl
 #align fin.add_nat_cast Fin.addNat_cast
+-/
 
+#print Fin.cast_addNat_left /-
 theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (addNat m i) = addNat m (cast (add_right_cancel h) i) :=
   ext rfl
 #align fin.cast_add_nat_left Fin.cast_addNat_left
+-/
 
+#print Fin.cast_addNat_right /-
 @[simp]
 theorem cast_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
     cast h (addNat m' i) = addNat m i :=
   ext <| (congr_arg ((· + ·) (i : ℕ)) (add_left_cancel h) : _)
 #align fin.cast_add_nat_right Fin.cast_addNat_right
+-/
 
 #print Fin.natAdd /-
 /-- `nat_add n i` adds `n` to `i` "on the left". -/
@@ -1557,80 +1767,110 @@ def natAdd (n) {m} : Fin m ↪o Fin (n + m) :=
 #align fin.nat_add Fin.natAdd
 -/
 
+#print Fin.coe_natAdd /-
 @[simp]
 theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAdd n i : ℕ) = n + i :=
   rfl
 #align fin.coe_nat_add Fin.coe_natAdd
+-/
 
+#print Fin.natAdd_mk /-
 @[simp]
 theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAdd n ⟨i, hi⟩ = ⟨n + i, add_lt_add_left hi n⟩ :=
   rfl
 #align fin.nat_add_mk Fin.natAdd_mk
+-/
 
+#print Fin.le_coe_natAdd /-
 theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAdd m i :=
   Nat.le_add_right _ _
 #align fin.le_coe_nat_add Fin.le_coe_natAdd
+-/
 
+#print Fin.natAdd_zero /-
 theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRelEmbedding := by ext;
   apply zero_add
 #align fin.nat_add_zero Fin.natAdd_zero
+-/
 
+#print Fin.natAdd_cast /-
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
 theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
     natAdd m (cast h i) = cast (congr_arg _ h) (natAdd m i) :=
   ext rfl
 #align fin.nat_add_cast Fin.natAdd_cast
+-/
 
+#print Fin.cast_natAdd_right /-
 theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
     cast h (natAdd m i) = natAdd m (cast (add_left_cancel h) i) :=
   ext rfl
 #align fin.cast_nat_add_right Fin.cast_natAdd_right
+-/
 
+#print Fin.cast_natAdd_left /-
 @[simp]
 theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
     cast h (natAdd m' i) = natAdd m i :=
   ext <| (congr_arg (· + (i : ℕ)) (add_right_cancel h) : _)
 #align fin.cast_nat_add_left Fin.cast_natAdd_left
+-/
 
+#print Fin.castAdd_natAdd /-
 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     castAdd p (natAdd m i) = cast (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
   ext rfl
 #align fin.cast_add_nat_add Fin.castAdd_natAdd
+-/
 
+#print Fin.natAdd_castAdd /-
 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     natAdd m (castAdd p i) = cast (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
   ext rfl
 #align fin.nat_add_cast_add Fin.natAdd_castAdd
+-/
 
+#print Fin.natAdd_natAdd /-
 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
     natAdd m (natAdd n i) = cast (add_assoc _ _ _) (natAdd (m + n) i) :=
   ext <| (add_assoc _ _ _).symm
 #align fin.nat_add_nat_add Fin.natAdd_natAdd
+-/
 
+#print Fin.cast_natAdd_zero /-
 @[simp]
 theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
     cast h (natAdd 0 i) = cast ((zero_add _).symm.trans h) i :=
   ext <| zero_add _
 #align fin.cast_nat_add_zero Fin.cast_natAdd_zero
+-/
 
+#print Fin.cast_natAdd /-
 @[simp]
 theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAdd n i) = addNat n i :=
   ext <| add_comm _ _
 #align fin.cast_nat_add Fin.cast_natAdd
+-/
 
+#print Fin.cast_addNat /-
 @[simp]
 theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNat m i) = natAdd m i :=
   ext <| add_comm _ _
 #align fin.cast_add_nat Fin.cast_addNat
+-/
 
+#print Fin.natAdd_last /-
 @[simp]
 theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
   rfl
 #align fin.nat_add_last Fin.natAdd_last
+-/
 
+#print Fin.natAdd_castSucc /-
 theorem natAdd_castSucc {m n : ℕ} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
   rfl
 #align fin.nat_add_cast_succ Fin.natAdd_castSucc
+-/
 
 end Succ
 
@@ -1641,9 +1881,11 @@ section Pred
 -/
 
 
+#print Fin.coe_pred /-
 @[simp]
 theorem coe_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : ℕ) = j - 1 := by cases j; rfl
 #align fin.coe_pred Fin.coe_pred
+-/
 
 #print Fin.succ_pred /-
 @[simp]
@@ -1653,14 +1895,18 @@ theorem succ_pred : ∀ (i : Fin (n + 1)) (h : i ≠ 0), (i.pred h).succ = i
 #align fin.succ_pred Fin.succ_pred
 -/
 
+#print Fin.pred_succ /-
 @[simp]
 theorem pred_succ (i : Fin n) {h : i.succ ≠ 0} : i.succ.pred h = i := by cases i; rfl
 #align fin.pred_succ Fin.pred_succ
+-/
 
+#print Fin.pred_eq_iff_eq_succ /-
 theorem pred_eq_iff_eq_succ {n : ℕ} (i : Fin (n + 1)) (hi : i ≠ 0) (j : Fin n) :
     i.pred hi = j ↔ i = j.succ :=
   ⟨fun h => by simp only [← h, Fin.succ_pred], fun h => by simp only [h, Fin.pred_succ]⟩
 #align fin.pred_eq_iff_eq_succ Fin.pred_eq_iff_eq_succ
+-/
 
 #print Fin.pred_mk_succ /-
 @[simp]
@@ -1680,15 +1926,19 @@ theorem pred_mk {n : ℕ} (i : ℕ) (h : i < n + 1) (w) :
 #align fin.pred_mk Fin.pred_mk
 -/
 
+#print Fin.pred_le_pred_iff /-
 @[simp]
 theorem pred_le_pred_iff {n : ℕ} {a b : Fin n.succ} {ha : a ≠ 0} {hb : b ≠ 0} :
     a.pred ha ≤ b.pred hb ↔ a ≤ b := by rw [← succ_le_succ_iff, succ_pred, succ_pred]
 #align fin.pred_le_pred_iff Fin.pred_le_pred_iff
+-/
 
+#print Fin.pred_lt_pred_iff /-
 @[simp]
 theorem pred_lt_pred_iff {n : ℕ} {a b : Fin n.succ} {ha : a ≠ 0} {hb : b ≠ 0} :
     a.pred ha < b.pred hb ↔ a < b := by rw [← succ_lt_succ_iff, succ_pred, succ_pred]
 #align fin.pred_lt_pred_iff Fin.pred_lt_pred_iff
+-/
 
 #print Fin.pred_inj /-
 @[simp]
@@ -1699,10 +1949,12 @@ theorem pred_inj : ∀ {a b : Fin (n + 1)} {ha : a ≠ 0} {hb : b ≠ 0}, a.pred
 #align fin.pred_inj Fin.pred_inj
 -/
 
+#print Fin.pred_one /-
 @[simp]
 theorem pred_one {n : ℕ} : Fin.pred (1 : Fin (n + 2)) (Ne.symm (ne_of_lt one_pos)) = 0 :=
   rfl
 #align fin.pred_one Fin.pred_one
+-/
 
 #print Fin.pred_add_one /-
 theorem pred_add_one (i : Fin (n + 2)) (h : (i : ℕ) < n + 1) :
@@ -1735,27 +1987,35 @@ theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
 #align fin.sub_nat_mk Fin.subNat_mk
 -/
 
+#print Fin.pred_castSucc_succ /-
 @[simp]
 theorem pred_castSucc_succ (i : Fin n) :
     pred (castSucc i.succ) (ne_of_gt (castSucc_pos i.succ_pos)) = i.cast_succ := by
   simp [eq_iff_veq]
 #align fin.pred_cast_succ_succ Fin.pred_castSucc_succ
+-/
 
+#print Fin.addNat_subNat /-
 @[simp]
 theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat m (subNat m i h) = i :=
   ext <| tsub_add_cancel_of_le h
 #align fin.add_nat_sub_nat Fin.addNat_subNat
+-/
 
+#print Fin.subNat_addNat /-
 @[simp]
 theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addNat m i) :
     subNat m (addNat m i) h = i :=
   ext <| add_tsub_cancel_right i m
 #align fin.sub_nat_add_nat Fin.subNat_addNat
+-/
 
+#print Fin.natAdd_subNat_cast /-
 @[simp]
 theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
     natAdd n (subNat n (cast (add_comm _ _) i) h) = i := by simp [← cast_add_nat]
 #align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_cast
+-/
 
 end Pred
 
@@ -1798,6 +2058,7 @@ section Rec
 -/
 
 
+#print Fin.succRec /-
 /-- Define `C n i` by induction on `i : fin n` interpreted as `(0 : fin (n - i)).succ.succ…`.
 This function has two arguments: `H0 n` defines `0`-th element `C (n+1) 0` of an `(n+1)`-tuple,
 and `Hs n i` defines `(i+1)`-st element of `(n+1)`-tuple based on `n`, `i`, and `i`-th element
@@ -1809,7 +2070,9 @@ def succRec {C : ∀ n, Fin n → Sort _} (H0 : ∀ n, C (succ n) 0)
   | succ n, ⟨0, _⟩ => H0 _
   | succ n, ⟨succ i, h⟩ => Hs _ _ (succ_rec ⟨i, lt_of_succ_lt_succ h⟩)
 #align fin.succ_rec Fin.succRec
+-/
 
+#print Fin.succRecOn /-
 /-- Define `C n i` by induction on `i : fin n` interpreted as `(0 : fin (n - i)).succ.succ…`.
 This function has two arguments: `H0 n` defines `0`-th element `C (n+1) 0` of an `(n+1)`-tuple,
 and `Hs n i` defines `(i+1)`-st element of `(n+1)`-tuple based on `n`, `i`, and `i`-th element
@@ -1821,18 +2084,24 @@ def succRecOn {n : ℕ} (i : Fin n) {C : ∀ n, Fin n → Sort _} (H0 : ∀ n, C
     (Hs : ∀ n i, C n i → C (succ n) i.succ) : C n i :=
   i.succRec H0 Hs
 #align fin.succ_rec_on Fin.succRecOn
+-/
 
+#print Fin.succRecOn_zero /-
 @[simp]
 theorem succRecOn_zero {C : ∀ n, Fin n → Sort _} {H0 Hs} (n) :
     @Fin.succRecOn (succ n) 0 C H0 Hs = H0 n :=
   rfl
 #align fin.succ_rec_on_zero Fin.succRecOn_zero
+-/
 
+#print Fin.succRecOn_succ /-
 @[simp]
 theorem succRecOn_succ {C : ∀ n, Fin n → Sort _} {H0 Hs} {n} (i : Fin n) :
     @Fin.succRecOn (succ n) i.succ C H0 Hs = Hs n i (Fin.succRecOn i H0 Hs) := by cases i <;> rfl
 #align fin.succ_rec_on_succ Fin.succRecOn_succ
+-/
 
+#print Fin.induction /-
 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
 and `hs` defines the inductive step using `C i.cast_succ`.
@@ -1846,19 +2115,25 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
   · refine' hs ⟨i, lt_of_succ_lt_succ hi⟩ _
     exact IH (lt_of_succ_lt hi)
 #align fin.induction Fin.induction
+-/
 
+#print Fin.induction_zero /-
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
     (hs : ∀ i : Fin n, C i.cast_succ → C i.succ) : (induction h0 hs : _) 0 = h0 :=
   rfl
 #align fin.induction_zero Fin.induction_zero
+-/
 
+#print Fin.induction_succ /-
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
     (hs : ∀ i : Fin n, C i.cast_succ → C i.succ) (i : Fin n) :
     (induction h0 hs : _) i.succ = hs i (induction h0 hs i.cast_succ) := by cases i <;> rfl
 #align fin.induction_succ Fin.induction_succ
+-/
 
+#print Fin.inductionOn /-
 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
 and `hs` defines the inductive step using `C i.cast_succ`.
@@ -1870,7 +2145,9 @@ def inductionOn (i : Fin (n + 1)) {C : Fin (n + 1) → Sort _} (h0 : C 0)
     (hs : ∀ i : Fin n, C i.cast_succ → C i.succ) : C i :=
   induction h0 hs i
 #align fin.induction_on Fin.inductionOn
+-/
 
+#print Fin.cases /-
 /-- Define `f : Π i : fin n.succ, C i` by separately handling the cases `i = 0` and
 `i = j.succ`, `j : fin n`. -/
 @[elab_as_elim]
@@ -1878,51 +2155,73 @@ def cases {C : Fin (succ n) → Sort _} (H0 : C 0) (Hs : ∀ i : Fin n, C i.succ
     ∀ i : Fin (succ n), C i :=
   induction H0 fun i _ => Hs i
 #align fin.cases Fin.cases
+-/
 
+#print Fin.cases_zero /-
 @[simp]
 theorem cases_zero {n} {C : Fin (succ n) → Sort _} {H0 Hs} : @Fin.cases n C H0 Hs 0 = H0 :=
   rfl
 #align fin.cases_zero Fin.cases_zero
+-/
 
+#print Fin.cases_succ /-
 @[simp]
 theorem cases_succ {n} {C : Fin (succ n) → Sort _} {H0 Hs} (i : Fin n) :
     @Fin.cases n C H0 Hs i.succ = Hs i := by cases i <;> rfl
 #align fin.cases_succ Fin.cases_succ
+-/
 
+#print Fin.cases_succ' /-
 @[simp]
 theorem cases_succ' {n} {C : Fin (succ n) → Sort _} {H0 Hs} {i : ℕ} (h : i + 1 < n + 1) :
     @Fin.cases n C H0 Hs ⟨i.succ, h⟩ = Hs ⟨i, lt_of_succ_lt_succ h⟩ := by cases i <;> rfl
 #align fin.cases_succ' Fin.cases_succ'
+-/
 
+#print Fin.forall_fin_succ /-
 theorem forall_fin_succ {P : Fin (n + 1) → Prop} : (∀ i, P i) ↔ P 0 ∧ ∀ i : Fin n, P i.succ :=
   ⟨fun H => ⟨H 0, fun i => H _⟩, fun ⟨H0, H1⟩ i => Fin.cases H0 H1 i⟩
 #align fin.forall_fin_succ Fin.forall_fin_succ
+-/
 
+#print Fin.exists_fin_succ /-
 theorem exists_fin_succ {P : Fin (n + 1) → Prop} : (∃ i, P i) ↔ P 0 ∨ ∃ i : Fin n, P i.succ :=
   ⟨fun ⟨i, h⟩ => Fin.cases Or.inl (fun i hi => Or.inr ⟨i, hi⟩) i h, fun h =>
     h.elim (fun h => ⟨0, h⟩) fun ⟨i, hi⟩ => ⟨i.succ, hi⟩⟩
 #align fin.exists_fin_succ Fin.exists_fin_succ
+-/
 
+#print Fin.forall_fin_one /-
 theorem forall_fin_one {p : Fin 1 → Prop} : (∀ i, p i) ↔ p 0 :=
   @Unique.forall_iff (Fin 1) _ p
 #align fin.forall_fin_one Fin.forall_fin_one
+-/
 
+#print Fin.exists_fin_one /-
 theorem exists_fin_one {p : Fin 1 → Prop} : (∃ i, p i) ↔ p 0 :=
   @Unique.exists_iff (Fin 1) _ p
 #align fin.exists_fin_one Fin.exists_fin_one
+-/
 
+#print Fin.forall_fin_two /-
 theorem forall_fin_two {p : Fin 2 → Prop} : (∀ i, p i) ↔ p 0 ∧ p 1 :=
   forall_fin_succ.trans <| and_congr_right fun _ => forall_fin_one
 #align fin.forall_fin_two Fin.forall_fin_two
+-/
 
+#print Fin.exists_fin_two /-
 theorem exists_fin_two {p : Fin 2 → Prop} : (∃ i, p i) ↔ p 0 ∨ p 1 :=
   exists_fin_succ.trans <| or_congr_right exists_fin_one
 #align fin.exists_fin_two Fin.exists_fin_two
+-/
 
+#print Fin.fin_two_eq_of_eq_zero_iff /-
 theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b := by revert a b;
   simp [forall_fin_two]
 #align fin.fin_two_eq_of_eq_zero_iff Fin.fin_two_eq_of_eq_zero_iff
+-/
 
+#print Fin.reverseInduction /-
 /--
 Define `C i` by reverse induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `hlast` handles the base case on `C (fin.last n)`,
@@ -1942,14 +2241,18 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
       cast (by rw [hi]) (hs _ (reverse_induction j.succ))
 termination_by' ⟨_, measure_wf fun i : Fin (n + 1) => n + 1 - i⟩
 #align fin.reverse_induction Fin.reverseInduction
+-/
 
+#print Fin.reverse_induction_last /-
 @[simp]
 theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) :
     (reverseInduction h0 hs (Fin.last n) : C (Fin.last n)) = h0 := by
   rw [reverse_induction] <;> simp
 #align fin.reverse_induction_last Fin.reverse_induction_last
+-/
 
+#print Fin.reverse_induction_castSucc /-
 @[simp]
 theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) (i : Fin n) :
@@ -1959,7 +2262,9 @@ theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 :
   cases i
   rfl
 #align fin.reverse_induction_cast_succ Fin.reverse_induction_castSucc
+-/
 
+#print Fin.lastCases /-
 /-- Define `f : Π i : fin n.succ, C i` by separately handling the cases `i = fin.last n` and
 `i = j.cast_succ`, `j : fin n`. -/
 @[elab_as_elim]
@@ -1967,21 +2272,27 @@ def lastCases {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) (i : Fin (n + 1)) : C i :=
   reverseInduction hlast (fun i _ => hcast i) i
 #align fin.last_cases Fin.lastCases
+-/
 
+#print Fin.lastCases_last /-
 @[simp]
 theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) :
     (Fin.lastCases hlast hcast (Fin.last n) : C (Fin.last n)) = hlast :=
   reverse_induction_last _ _
 #align fin.last_cases_last Fin.lastCases_last
+-/
 
+#print Fin.lastCases_castSucc /-
 @[simp]
 theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) (i : Fin n) :
     (Fin.lastCases hlast hcast (Fin.castSucc i) : C (Fin.castSucc i)) = hcast i :=
   reverse_induction_castSucc _ _ _
 #align fin.last_cases_cast_succ Fin.lastCases_castSucc
+-/
 
+#print Fin.addCases /-
 /-- Define `f : Π i : fin (m + n), C i` by separately handling the cases `i = cast_add n i`,
 `j : fin m` and `i = nat_add m j`, `j : fin n`. -/
 @[elab_as_elim]
@@ -1990,7 +2301,9 @@ def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd
   if hi : (i : ℕ) < m then Eq.recOn (castAdd_castLT n i hi) (hleft (castLT i hi))
   else Eq.recOn (natAdd_subNat_cast (le_of_not_lt hi)) (hright _)
 #align fin.add_cases Fin.addCases
+-/
 
+#print Fin.addCases_left /-
 @[simp]
 theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
     (hright : ∀ i, C (natAdd m i)) (i : Fin m) :
@@ -2000,7 +2313,9 @@ theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C
   rw [add_cases, dif_pos (cast_add_lt _ _)]
   rfl
 #align fin.add_cases_left Fin.addCases_left
+-/
 
+#print Fin.addCases_right /-
 @[simp]
 theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
     (hright : ∀ i, C (natAdd m i)) (i : Fin n) :
@@ -2011,9 +2326,11 @@ theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i,
   refine' eq_of_hEq ((eq_rec_hEq _ _).trans _); congr 1
   simp
 #align fin.add_cases_right Fin.addCases_right
+-/
 
 end Rec
 
+#print Fin.liftFun_iff_succ /-
 theorem liftFun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=
   by
@@ -2027,32 +2344,41 @@ theorem liftFun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {
       rcases hij.eq_or_lt with (rfl | hlt)
       exacts [H j, trans (ihj hlt) (H j)]
 #align fin.lift_fun_iff_succ Fin.liftFun_iff_succ
+-/
 
+#print Fin.strictMono_iff_lt_succ /-
 /-- A function `f` on `fin (n + 1)` is strictly monotone if and only if `f i < f (i + 1)`
 for all `i`. -/
 theorem strictMono_iff_lt_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     StrictMono f ↔ ∀ i : Fin n, f i.cast_succ < f i.succ :=
   liftFun_iff_succ (· < ·)
 #align fin.strict_mono_iff_lt_succ Fin.strictMono_iff_lt_succ
+-/
 
+#print Fin.monotone_iff_le_succ /-
 /-- A function `f` on `fin (n + 1)` is monotone if and only if `f i ≤ f (i + 1)` for all `i`. -/
 theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     Monotone f ↔ ∀ i : Fin n, f i.cast_succ ≤ f i.succ :=
   monotone_iff_forall_lt.trans <| liftFun_iff_succ (· ≤ ·)
 #align fin.monotone_iff_le_succ Fin.monotone_iff_le_succ
+-/
 
+#print Fin.strictAnti_iff_succ_lt /-
 /-- A function `f` on `fin (n + 1)` is strictly antitone if and only if `f (i + 1) < f i`
 for all `i`. -/
 theorem strictAnti_iff_succ_lt {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     StrictAnti f ↔ ∀ i : Fin n, f i.succ < f i.cast_succ :=
   liftFun_iff_succ (· > ·)
 #align fin.strict_anti_iff_succ_lt Fin.strictAnti_iff_succ_lt
+-/
 
+#print Fin.antitone_iff_succ_le /-
 /-- A function `f` on `fin (n + 1)` is antitone if and only if `f (i + 1) ≤ f i` for all `i`. -/
 theorem antitone_iff_succ_le {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     Antitone f ↔ ∀ i : Fin n, f i.succ ≤ f i.cast_succ :=
   antitone_iff_forall_lt.trans <| liftFun_iff_succ (· ≥ ·)
 #align fin.antitone_iff_succ_le Fin.antitone_iff_succ_le
+-/
 
 section AddGroup
 
@@ -2075,9 +2401,11 @@ instance (n : ℕ) [NeZero n] : AddCommGroup (Fin n) :=
       Fin.ext <| show (a + (n - b)) % n = (a + (n - b) % n) % n by simp
     sub := Fin.sub }
 
+#print Fin.coe_neg /-
 protected theorem coe_neg (a : Fin n) : ((-a : Fin n) : ℕ) = (n - a) % n :=
   rfl
 #align fin.coe_neg Fin.coe_neg
+-/
 
 #print Fin.coe_sub /-
 protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : ℕ) = (a + (n - b)) % n := by
@@ -2091,6 +2419,7 @@ theorem coe_fin_one (a : Fin 1) : ↑a = 0 := by rw [Subsingleton.elim a 0, Fin.
 #align fin.coe_fin_one Fin.coe_fin_one
 -/
 
+#print Fin.coe_neg_one /-
 @[simp]
 theorem coe_neg_one : ↑(-1 : Fin (n + 1)) = n :=
   by
@@ -2099,7 +2428,9 @@ theorem coe_neg_one : ↑(-1 : Fin (n + 1)) = n :=
   rw [Fin.coe_neg, Fin.val_one, Nat.succ_sub_one, Nat.mod_eq_of_lt]
   constructor
 #align fin.coe_neg_one Fin.coe_neg_one
+-/
 
+#print Fin.coe_sub_one /-
 theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a - 1 :=
   by
   cases n
@@ -2110,6 +2441,7 @@ theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a
   rw [add_comm ↑a, add_le_add_iff_left, Nat.one_le_iff_ne_zero]
   rwa [Fin.ext_iff] at h 
 #align fin.coe_sub_one Fin.coe_sub_one
+-/
 
 #print Fin.coe_sub_iff_le /-
 theorem coe_sub_iff_le {n : ℕ} {a b : Fin n} : (↑(a - b) : ℕ) = a - b ↔ b ≤ a :=
@@ -2139,6 +2471,7 @@ theorem coe_sub_iff_lt {n : ℕ} {a b : Fin n} : (↑(a - b) : ℕ) = n + a - b
 #align fin.coe_sub_iff_lt Fin.coe_sub_iff_lt
 -/
 
+#print Fin.lt_sub_one_iff /-
 @[simp]
 theorem lt_sub_one_iff {n : ℕ} {k : Fin (n + 2)} : k < k - 1 ↔ k = 0 :=
   by
@@ -2149,7 +2482,9 @@ theorem lt_sub_one_iff {n : ℕ} {k : Fin (n + 2)} : k < k - 1 ↔ k = 0 :=
   simp [lt_iff_coe_lt_coe, ext_iff, Fin.coe_sub, succ_eq_add_one, this,
     mod_eq_of_lt ((lt_succ_self _).trans hk)]
 #align fin.lt_sub_one_iff Fin.lt_sub_one_iff
+-/
 
+#print Fin.le_sub_one_iff /-
 @[simp]
 theorem le_sub_one_iff {n : ℕ} {k : Fin (n + 1)} : k ≤ k - 1 ↔ k = 0 :=
   by
@@ -2159,11 +2494,14 @@ theorem le_sub_one_iff {n : ℕ} {k : Fin (n + 1)} : k ≤ k - 1 ↔ k = 0 :=
     sub_eq_iff_eq_add]
   simp
 #align fin.le_sub_one_iff Fin.le_sub_one_iff
+-/
 
+#print Fin.sub_one_lt_iff /-
 @[simp]
 theorem sub_one_lt_iff {n : ℕ} {k : Fin (n + 1)} : k - 1 < k ↔ 0 < k :=
   not_iff_not.1 <| by simp only [not_lt, le_sub_one_iff, le_zero_iff]
 #align fin.sub_one_lt_iff Fin.sub_one_lt_iff
+-/
 
 #print Fin.last_sub /-
 theorem last_sub (i : Fin (n + 1)) : last n - i = i.rev :=
@@ -2175,24 +2513,31 @@ end AddGroup
 
 section SuccAbove
 
+#print Fin.succAbove_aux /-
 theorem succAbove_aux (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
   (castSucc : Fin n ↪o _).StrictMono.ite (succEmbedding n).StrictMono
     (fun i j hij hj => lt_trans ((castSucc : Fin n ↪o _).lt_iff_lt.2 hij) hj) fun i =>
     (castSucc_lt_succ i).le
 #align fin.succ_above_aux Fin.succAbove_aux
+-/
 
+#print Fin.succAbove /-
 /-- `succ_above p i` embeds `fin n` into `fin (n + 1)` with a hole around `p`. -/
 def succAbove (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
   OrderEmbedding.ofStrictMono _ p.succAbove_aux
 #align fin.succ_above Fin.succAbove
+-/
 
+#print Fin.succAbove_below /-
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
 theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
     p.succAbove i = i.cast_succ := by rw [succ_above]; exact if_pos h
 #align fin.succ_above_below Fin.succAbove_below
+-/
 
+#print Fin.succAbove_ne_zero_zero /-
 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 :=
   by
@@ -2200,50 +2545,68 @@ theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.s
   · rfl
   · exact bot_lt_iff_ne_bot.mpr ha
 #align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zero
+-/
 
+#print Fin.succAbove_eq_zero_iff /-
 theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) :
     a.succAbove b = 0 ↔ b = 0 := by
   simp only [← succ_above_ne_zero_zero ha, OrderEmbedding.eq_iff_eq]
 #align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iff
+-/
 
+#print Fin.succAbove_ne_zero /-
 theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) (hb : b ≠ 0) :
     a.succAbove b ≠ 0 :=
   mt (succAbove_eq_zero_iff ha).mp hb
 #align fin.succ_above_ne_zero Fin.succAbove_ne_zero
+-/
 
+#print Fin.succAbove_zero /-
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around zero embeds by `succ`. -/
 @[simp]
 theorem succAbove_zero : ⇑(succAbove (0 : Fin (n + 1))) = Fin.succ :=
   rfl
 #align fin.succ_above_zero Fin.succAbove_zero
+-/
 
+#print Fin.succAbove_last /-
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around `last n` embeds by `cast_succ`. -/
 @[simp]
 theorem succAbove_last : succAbove (Fin.last n) = castSucc := by ext;
   simp only [succ_above_below, cast_succ_lt_last]
 #align fin.succ_above_last Fin.succAbove_last
+-/
 
+#print Fin.succAbove_last_apply /-
 theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_succ := by
   rw [succ_above_last]
 #align fin.succ_above_last_apply Fin.succAbove_last_apply
+-/
 
+#print Fin.succAbove_above /-
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
 theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
     p.succAbove i = i.succ := by simp [succ_above, h.not_lt]
 #align fin.succ_above_above Fin.succAbove_above
+-/
 
+#print Fin.succAbove_lt_ge /-
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p ≤ i.cast_succ :=
   lt_or_ge (castSucc i) p
 #align fin.succ_above_lt_ge Fin.succAbove_lt_ge
+-/
 
+#print Fin.succAbove_lt_gt /-
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
   Or.cases_on (succAbove_lt_ge p i) (fun h => Or.inl h) fun h =>
     Or.inr (lt_of_le_of_lt h (castSucc_lt_succ i))
 #align fin.succ_above_lt_gt Fin.succAbove_lt_gt
+-/
 
+#print Fin.succAbove_lt_iff /-
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
 @[simp]
@@ -2259,7 +2622,9 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
     rw [succ_above_below _ _ h]
     exact h
 #align fin.succ_above_lt_iff Fin.succAbove_lt_iff
+-/
 
+#print Fin.lt_succAbove_iff /-
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
 theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p ≤ i.cast_succ :=
@@ -2274,7 +2639,9 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
     rw [succ_above_above _ _ h]
     exact lt_of_le_of_lt h (cast_succ_lt_succ i)
 #align fin.lt_succ_above_iff Fin.lt_succAbove_iff
+-/
 
+#print Fin.succAbove_ne /-
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 never results in `p` itself -/
 theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
@@ -2284,7 +2651,9 @@ theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
   · simpa [lt_irrefl, ← succ_above_below _ _ H, Eq] using H
   · simpa [← succ_above_above _ _ (le_of_not_lt H), Eq] using cast_succ_lt_succ i
 #align fin.succ_above_ne Fin.succAbove_ne
+-/
 
+#print Fin.succAbove_pos /-
 /-- Embedding a positive `fin n` results in a positive fin (n + 1)` -/
 theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i :=
   by
@@ -2292,35 +2661,47 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
   · simpa [succ_above_below _ _ H] using cast_succ_pos h
   · simp [succ_above_above _ _ (le_of_not_lt H)]
 #align fin.succ_above_pos Fin.succAbove_pos
+-/
 
+#print Fin.succAbove_castLT /-
 @[simp]
 theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
     (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLT hx) = x := by
   rw [succ_above_below, cast_succ_cast_lt]; exact h
 #align fin.succ_above_cast_lt Fin.succAbove_castLT
+-/
 
+#print Fin.succAbove_pred /-
 @[simp]
 theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
     x.succAbove (y.pred hy) = y := by rw [succ_above_above, succ_pred];
   simpa [le_iff_coe_le_coe] using Nat.le_pred_of_lt h
 #align fin.succ_above_pred Fin.succAbove_pred
+-/
 
+#print Fin.castLT_succAbove /-
 theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
     (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
     (y.succAbove x).castLT h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
 #align fin.cast_lt_succ_above Fin.castLT_succAbove
+-/
 
+#print Fin.pred_succAbove /-
 theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
     (h' : y.succAbove x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
     (y.succAbove x).pred h' = x := by simp only [succ_above_above _ _ h, pred_succ]
 #align fin.pred_succ_above Fin.pred_succAbove
+-/
 
+#print Fin.exists_succAbove_eq /-
 theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x :=
   by
   cases' h.lt_or_lt with hlt hlt
   exacts [⟨_, succ_above_cast_lt hlt⟩, ⟨_, succ_above_pred hlt⟩]
 #align fin.exists_succ_above_eq Fin.exists_succAbove_eq
+-/
 
+#print Fin.exists_succAbove_eq_iff /-
 @[simp]
 theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y) ↔ y ≠ x :=
   by
@@ -2328,54 +2709,74 @@ theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y)
   rintro ⟨y, rfl⟩
   exact succ_above_ne _ _
 #align fin.exists_succ_above_eq_iff Fin.exists_succAbove_eq_iff
+-/
 
+#print Fin.range_succAbove /-
 /-- The range of `p.succ_above` is everything except `p`. -/
 @[simp]
 theorem range_succAbove (p : Fin (n + 1)) : Set.range p.succAbove = {p}ᶜ :=
   Set.ext fun _ => exists_succAbove_eq_iff
 #align fin.range_succ_above Fin.range_succAbove
+-/
 
+#print Fin.range_succ /-
 @[simp]
 theorem range_succ (n : ℕ) : Set.range (Fin.succ : Fin n → Fin (n + 1)) = {0}ᶜ :=
   range_succAbove 0
 #align fin.range_succ Fin.range_succ
+-/
 
+#print Fin.exists_succ_eq_iff /-
 @[simp]
 theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠ 0 :=
   @exists_succAbove_eq_iff n 0 x
 #align fin.exists_succ_eq_iff Fin.exists_succ_eq_iff
+-/
 
+#print Fin.succAbove_right_injective /-
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
   (succAbove x).Injective
 #align fin.succ_above_right_injective Fin.succAbove_right_injective
+-/
 
+#print Fin.succAbove_right_inj /-
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b ↔ a = b :=
   succAbove_right_injective.eq_iff
 #align fin.succ_above_right_inj Fin.succAbove_right_inj
+-/
 
+#print Fin.succAbove_left_injective /-
 /-- `succ_above` is injective at the pivot -/
 theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
   simpa [range_succ_above] using congr_arg (fun f : Fin n ↪o Fin (n + 1) => Set.range fᶜ) h
 #align fin.succ_above_left_injective Fin.succAbove_left_injective
+-/
 
+#print Fin.succAbove_left_inj /-
 /-- `succ_above` is injective at the pivot -/
 @[simp]
 theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAbove = y.succAbove ↔ x = y :=
   succAbove_left_injective.eq_iff
 #align fin.succ_above_left_inj Fin.succAbove_left_inj
+-/
 
+#print Fin.zero_succAbove /-
 @[simp]
 theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i.succ :=
   rfl
 #align fin.zero_succ_above Fin.zero_succAbove
+-/
 
+#print Fin.succ_succAbove_zero /-
 @[simp]
 theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove 0 = 0 :=
   succAbove_below _ _ (succ_pos _)
 #align fin.succ_succ_above_zero Fin.succ_succAbove_zero
+-/
 
+#print Fin.succ_succAbove_succ /-
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
     i.succ.succAbove j.succ = (i.succAbove j).succ :=
@@ -2389,12 +2790,16 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
     ext
     simp [succ_above_above _ _ h, succ_above_above _ _ h']
 #align fin.succ_succ_above_succ Fin.succ_succAbove_succ
+-/
 
+#print Fin.one_succAbove_zero /-
 @[simp]
 theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
   succ_succAbove_zero 0
 #align fin.one_succ_above_zero Fin.one_succAbove_zero
+-/
 
+#print Fin.succ_succAbove_one /-
 /-- By moving `succ` to the outside of this expression, we create opportunities for further
 simplification using `succ_above_zero` or `succ_succ_above_zero`. -/
 @[simp]
@@ -2402,16 +2807,21 @@ theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
     i.succ.succAbove 1 = (i.succAbove 0).succ := by
   rw [← succ_succ_above_succ i 0, succ_zero_eq_one]
 #align fin.succ_succ_above_one Fin.succ_succAbove_one
+-/
 
+#print Fin.one_succAbove_succ /-
 @[simp]
 theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j.succ = j.succ.succ :=
   succ_succAbove_succ 0 j
 #align fin.one_succ_above_succ Fin.one_succAbove_succ
+-/
 
+#print Fin.one_succAbove_one /-
 @[simp]
 theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 :=
   succ_succAbove_succ 0 0
 #align fin.one_succ_above_one Fin.one_succAbove_one
+-/
 
 end SuccAbove
 
@@ -2425,6 +2835,7 @@ def predAbove (p : Fin n) (i : Fin (n + 1)) : Fin n :=
 #align fin.pred_above Fin.predAbove
 -/
 
+#print Fin.predAbove_right_monotone /-
 theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H =>
   by
   dsimp [pred_above]
@@ -2438,7 +2849,9 @@ theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H
   · simp at ha ; exact le_pred_of_lt (lt_of_le_of_lt ha hb)
   · exact H
 #align fin.pred_above_right_monotone Fin.predAbove_right_monotone
+-/
 
+#print Fin.predAbove_left_monotone /-
 theorem predAbove_left_monotone (i : Fin (n + 1)) : Monotone fun p => predAbove p i := fun a b H =>
   by
   dsimp [pred_above]
@@ -2448,6 +2861,7 @@ theorem predAbove_left_monotone (i : Fin (n + 1)) : Monotone fun p => predAbove
   · have : b < a := cast_succ_lt_cast_succ_iff.mpr (hb.trans_le (le_of_not_gt ha))
     exact absurd H this.not_le
 #align fin.pred_above_left_monotone Fin.predAbove_left_monotone
+-/
 
 #print Fin.castPred /-
 /-- `cast_pred` embeds `i : fin (n + 2)` into `fin (n + 1)`
@@ -2457,10 +2871,12 @@ def castPred (i : Fin (n + 2)) : Fin (n + 1) :=
 #align fin.cast_pred Fin.castPred
 -/
 
+#print Fin.castPred_zero /-
 @[simp]
 theorem castPred_zero : castPred (0 : Fin (n + 2)) = 0 :=
   rfl
 #align fin.cast_pred_zero Fin.castPred_zero
+-/
 
 #print Fin.castPred_one /-
 @[simp]
@@ -2468,6 +2884,7 @@ theorem castPred_one : castPred (1 : Fin (n + 2)) = 1 := by cases n; apply Subsi
 #align fin.cast_pred_one Fin.castPred_one
 -/
 
+#print Fin.predAbove_zero /-
 @[simp]
 theorem predAbove_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred hi :=
   by
@@ -2475,6 +2892,7 @@ theorem predAbove_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred
   rw [dif_pos]
   exact (pos_iff_ne_zero _).mpr hi
 #align fin.pred_above_zero Fin.predAbove_zero
+-/
 
 #print Fin.castPred_last /-
 @[simp]
@@ -2502,12 +2920,14 @@ theorem coe_castPred {n : ℕ} (a : Fin (n + 2)) (hx : a < Fin.last _) : (a.cast
 #align fin.coe_cast_pred Fin.coe_castPred
 -/
 
+#print Fin.predAbove_below /-
 theorem predAbove_below (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_succ) :
     p.predAbove i = i.cast_pred :=
   by
   have : i ≤ (last n).cast_succ := h.trans p.le_last
   simp [pred_above, cast_pred, h.not_lt, this.not_lt]
 #align fin.pred_above_below Fin.predAbove_below
+-/
 
 #print Fin.predAbove_last /-
 @[simp]
@@ -2516,18 +2936,25 @@ theorem predAbove_last : predAbove (Fin.last n) = castPred :=
 #align fin.pred_above_last Fin.predAbove_last
 -/
 
+#print Fin.predAbove_last_apply /-
 theorem predAbove_last_apply (i : Fin n) : predAbove (Fin.last n) i = i.cast_pred := by
   rw [pred_above_last]
 #align fin.pred_above_last_apply Fin.predAbove_last_apply
+-/
 
+#print Fin.predAbove_above /-
 theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
     p.predAbove i = i.pred (p.cast_succ.zero_le.trans_lt h).Ne.symm := by simp [pred_above, h]
 #align fin.pred_above_above Fin.predAbove_above
+-/
 
+#print Fin.castPred_monotone /-
 theorem castPred_monotone : Monotone (@castPred n) :=
   predAbove_right_monotone (last _)
 #align fin.cast_pred_monotone Fin.castPred_monotone
+-/
 
+#print Fin.succAbove_predAbove /-
 /-- Sending `fin (n+1)` to `fin n` by subtracting one from anything above `p`
 then back to `fin (n+1)` with a gap around `p` is the identity away from `p`. -/
 @[simp]
@@ -2548,7 +2975,9 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
       simp only [pred, Fin.mk_lt_mk, not_lt]
       exact Nat.le_pred_of_lt (Nat.lt_of_le_and_ne H (Ne.symm h))
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
+-/
 
+#print Fin.predAbove_succAbove /-
 /-- Sending `fin n` into `fin (n + 1)` with a gap at `p`
 then back to `fin n` by subtracting one from anything above `p` is the identity. -/
 @[simp]
@@ -2568,12 +2997,16 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
     · simp_rw [if_neg h]
       exact lt_succ_iff.mpr (not_lt.mp h)
 #align fin.pred_above_succ_above Fin.predAbove_succAbove
+-/
 
+#print Fin.castSucc_pred_eq_pred_castSucc /-
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
     (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' := by
   cases a; rfl
 #align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSucc
+-/
 
+#print Fin.pred_succAbove_pred /-
 /-- `pred` commutes with `succ_above`. -/
 theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
     (hk := succAbove_ne_zero ha hb) : (a.pred ha).succAbove (b.pred hb) = (a.succAbove b).pred hk :=
@@ -2588,6 +3021,7 @@ theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (
     · rwa [this, Fin.pred_inj, Fin.succAbove_above]
     · rwa [cast_succ_pred_eq_pred_cast_succ, Fin.pred_le_pred_iff]
 #align fin.pred_succ_above_pred Fin.pred_succAbove_pred
+-/
 
 #print Fin.succ_predAbove_succ /-
 /-- `succ` commutes with `pred_above`. -/
@@ -2619,17 +3053,21 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ
 -/
 
+#print Fin.castPred_castSucc /-
 @[simp]
 theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
   simp [cast_pred, pred_above, le_last]
 #align fin.cast_pred_cast_succ Fin.castPred_castSucc
+-/
 
+#print Fin.castSucc_castPred /-
 theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSucc i.cast_pred = i :=
   by
   rw [cast_pred, pred_above, dif_neg]
   · simp [Fin.eq_iff_veq]
   · exact h.not_le
 #align fin.cast_succ_cast_pred Fin.castSucc_castPred
+-/
 
 #print Fin.coe_castPred_le_self /-
 theorem coe_castPred_le_self (i : Fin (n + 2)) : (i.cast_pred : ℕ) ≤ i :=
@@ -2673,15 +3111,19 @@ def clamp (n m : ℕ) : Fin (m + 1) :=
 #align fin.clamp Fin.clamp
 -/
 
+#print Fin.coe_clamp /-
 @[simp]
 theorem coe_clamp (n m : ℕ) : (clamp n m : ℕ) = min n m :=
   Nat.mod_eq_of_lt <| Nat.lt_succ_iff.mpr <| min_le_right _ _
 #align fin.coe_clamp Fin.coe_clamp
+-/
 
+#print Fin.coe_ofNat_eq_mod /-
 @[simp]
 theorem coe_ofNat_eq_mod (m n : ℕ) [NeZero m] : ((n : Fin m) : ℕ) = n % m :=
   rfl
 #align fin.coe_of_nat_eq_mod Fin.coe_ofNat_eq_mod
+-/
 
 section Mul
 
@@ -2727,14 +3169,18 @@ protected theorem one_mul [NeZero n] (k : Fin n) : (1 : Fin n) * k = k := by
 #align fin.one_mul Fin.one_mul
 -/
 
+#print Fin.mul_zero /-
 @[simp]
 protected theorem mul_zero [NeZero n] (k : Fin n) : k * 0 = 0 := by simp [eq_iff_veq, mul_def]
 #align fin.mul_zero Fin.mul_zero
+-/
 
+#print Fin.zero_mul /-
 @[simp]
 protected theorem zero_mul [NeZero n] (k : Fin n) : (0 : Fin n) * k = 0 := by
   simp [eq_iff_veq, mul_def]
 #align fin.zero_mul Fin.zero_mul
+-/
 
 end Mul
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -2014,7 +2014,7 @@ theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i,
 
 end Rec
 
-theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
+theorem liftFun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=
   by
   constructor
@@ -2026,32 +2026,32 @@ theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r]
       rw [← le_cast_succ_iff] at hij 
       rcases hij.eq_or_lt with (rfl | hlt)
       exacts [H j, trans (ihj hlt) (H j)]
-#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succ
+#align fin.lift_fun_iff_succ Fin.liftFun_iff_succ
 
 /-- A function `f` on `fin (n + 1)` is strictly monotone if and only if `f i < f (i + 1)`
 for all `i`. -/
 theorem strictMono_iff_lt_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     StrictMono f ↔ ∀ i : Fin n, f i.cast_succ < f i.succ :=
-  lift_fun_iff_succ (· < ·)
+  liftFun_iff_succ (· < ·)
 #align fin.strict_mono_iff_lt_succ Fin.strictMono_iff_lt_succ
 
 /-- A function `f` on `fin (n + 1)` is monotone if and only if `f i ≤ f (i + 1)` for all `i`. -/
 theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     Monotone f ↔ ∀ i : Fin n, f i.cast_succ ≤ f i.succ :=
-  monotone_iff_forall_lt.trans <| lift_fun_iff_succ (· ≤ ·)
+  monotone_iff_forall_lt.trans <| liftFun_iff_succ (· ≤ ·)
 #align fin.monotone_iff_le_succ Fin.monotone_iff_le_succ
 
 /-- A function `f` on `fin (n + 1)` is strictly antitone if and only if `f (i + 1) < f i`
 for all `i`. -/
 theorem strictAnti_iff_succ_lt {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     StrictAnti f ↔ ∀ i : Fin n, f i.succ < f i.cast_succ :=
-  lift_fun_iff_succ (· > ·)
+  liftFun_iff_succ (· > ·)
 #align fin.strict_anti_iff_succ_lt Fin.strictAnti_iff_succ_lt
 
 /-- A function `f` on `fin (n + 1)` is antitone if and only if `f (i + 1) ≤ f i` for all `i`. -/
 theorem antitone_iff_succ_le {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     Antitone f ↔ ∀ i : Fin n, f i.succ ≤ f i.cast_succ :=
-  antitone_iff_forall_lt.trans <| lift_fun_iff_succ (· ≥ ·)
+  antitone_iff_forall_lt.trans <| liftFun_iff_succ (· ≥ ·)
 #align fin.antitone_iff_succ_le Fin.antitone_iff_succ_le
 
 section AddGroup
@@ -2435,7 +2435,6 @@ theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H
     calc
       _ ≤ _ := Nat.pred_le _
       _ ≤ _ := H
-      
   · simp at ha ; exact le_pred_of_lt (lt_of_le_of_lt ha hb)
   · exact H
 #align fin.pred_above_right_monotone Fin.predAbove_right_monotone

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -1187,7 +1187,7 @@ theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by s
 #align fin.cast_le_zero Fin.castLE_zero
 
 @[simp]
-theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i : ℕ) < n } :=
+theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = {i | (i : ℕ) < n} :=
   Set.ext fun x => ⟨fun ⟨y, hy⟩ => hy ▸ y.2, fun hx => ⟨⟨x, hx⟩, Fin.ext rfl⟩⟩
 #align fin.range_cast_le Fin.range_castLE
 
@@ -1484,7 +1484,7 @@ theorem lt_succ : a.cast_succ < a.succ := by
 #align fin.lt_succ Fin.lt_succ
 
 @[simp]
-theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = { i | (i : ℕ) < n } :=
+theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = {i | (i : ℕ) < n} :=
   range_castLE _
 #align fin.range_cast_succ Fin.range_castSucc
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -662,7 +662,7 @@ theorem coe_orderIso_apply (e : Fin n ≃o Fin m) (i : Fin n) : (e i : ℕ) = i
   induction' i using Nat.strong_induction_on with i h
   refine' le_antisymm (forall_lt_iff_le.1 fun j hj => _) (forall_lt_iff_le.1 fun j hj => _)
   · have := e.symm.lt_iff_lt.2 (mk_lt_of_lt_coe hj)
-    rw [e.symm_apply_apply] at this
+    rw [e.symm_apply_apply] at this 
     convert this
     simpa using h _ this (e.symm _).is_lt
   · rwa [← h j hj (hj.trans hi), ← lt_iff_coe_lt_coe, e.lt_iff_lt]
@@ -870,7 +870,7 @@ theorem mk_bit1 {m n : ℕ} [NeZero n] (h : bit1 m < n) :
       (bit1 ⟨m, (Nat.le_add_right m m).trans_lt ((m + m).lt_succ_self.trans h)⟩ : Fin _) :=
   by
   ext
-  simp only [bit1, bit0] at h
+  simp only [bit1, bit0] at h 
   simp only [bit1, bit0, coe_add, coe_one', coe_mk, ← Nat.add_mod, Nat.mod_eq_of_lt h]
 #align fin.mk_bit1 Fin.mk_bit1
 -/
@@ -951,7 +951,7 @@ theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) <
   by
   cases n
   · exact absurd h (Nat.not_lt_zero _)
-  · rw [lt_iff_coe_lt_coe, coe_last, ← add_lt_add_iff_right 1] at h
+  · rw [lt_iff_coe_lt_coe, coe_last, ← add_lt_add_iff_right 1] at h 
     rw [lt_iff_coe_lt_coe, coe_add, coe_zero, coe_one, Nat.mod_eq_of_lt h]
     exact Nat.zero_lt_succ _
 #align fin.add_one_pos Fin.add_one_pos
@@ -970,7 +970,7 @@ theorem zero_eq_one_iff [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 :=
   constructor
   · intro h
     have := congr_arg (coe : Fin n → ℕ) h
-    simp only [Fin.val_zero, ← Nat.dvd_iff_mod_eq_zero, Fin.val_one', @eq_comm _ 0] at this
+    simp only [Fin.val_zero, ← Nat.dvd_iff_mod_eq_zero, Fin.val_one', @eq_comm _ 0] at this 
     exact eq_one_of_dvd_one this
   · rintro rfl; rfl
 #align fin.zero_eq_one_iff Fin.zero_eq_one_iff
@@ -1939,8 +1939,8 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
         cases i
         rw [tsub_lt_tsub_iff_left_of_le] <;> simp [*, Nat.succ_le_iff]
       have hi : i = Fin.castSucc j := Fin.ext rfl
-      cast (by rw [hi]) (hs _ (reverse_induction j.succ))termination_by'
-  ⟨_, measure_wf fun i : Fin (n + 1) => n + 1 - i⟩
+      cast (by rw [hi]) (hs _ (reverse_induction j.succ))
+termination_by' ⟨_, measure_wf fun i : Fin (n + 1) => n + 1 - i⟩
 #align fin.reverse_induction Fin.reverseInduction
 
 @[simp]
@@ -2023,9 +2023,9 @@ theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r]
   · refine' fun H i => Fin.induction _ _
     · exact fun h => (h.not_le (zero_le i)).elim
     · intro j ihj hij
-      rw [← le_cast_succ_iff] at hij
+      rw [← le_cast_succ_iff] at hij 
       rcases hij.eq_or_lt with (rfl | hlt)
-      exacts[H j, trans (ihj hlt) (H j)]
+      exacts [H j, trans (ihj hlt) (H j)]
 #align fin.lift_fun_iff_succ Fin.lift_fun_iff_succ
 
 /-- A function `f` on `fin (n + 1)` is strictly monotone if and only if `f i < f (i + 1)`
@@ -2108,7 +2108,7 @@ theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a
   · simp [h]
   rw [sub_eq_add_neg, coe_add_eq_ite, coe_neg_one, if_pos, add_comm, add_tsub_add_eq_tsub_left]
   rw [add_comm ↑a, add_le_add_iff_left, Nat.one_le_iff_ne_zero]
-  rwa [Fin.ext_iff] at h
+  rwa [Fin.ext_iff] at h 
 #align fin.coe_sub_one Fin.coe_sub_one
 
 #print Fin.coe_sub_iff_le /-
@@ -2253,7 +2253,7 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
   · intro h
     cases' succ_above_lt_ge p i with H H
     · exact H
-    · rw [succ_above_above _ _ H] at h
+    · rw [succ_above_above _ _ H] at h 
       exact lt_trans (cast_succ_lt_succ i) h
   · intro h
     rw [succ_above_below _ _ h]
@@ -2267,7 +2267,7 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
   refine' Iff.intro _ _
   · intro h
     cases' succ_above_lt_ge p i with H H
-    · rw [succ_above_below _ _ H] at h
+    · rw [succ_above_below _ _ H] at h 
       exact le_of_lt h
     · exact H
   · intro h
@@ -2318,7 +2318,7 @@ theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
 theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x :=
   by
   cases' h.lt_or_lt with hlt hlt
-  exacts[⟨_, succ_above_cast_lt hlt⟩, ⟨_, succ_above_pred hlt⟩]
+  exacts [⟨_, succ_above_cast_lt hlt⟩, ⟨_, succ_above_pred hlt⟩]
 #align fin.exists_succ_above_eq Fin.exists_succAbove_eq
 
 @[simp]
@@ -2436,7 +2436,7 @@ theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H
       _ ≤ _ := Nat.pred_le _
       _ ≤ _ := H
       
-  · simp at ha; exact le_pred_of_lt (lt_of_le_of_lt ha hb)
+  · simp at ha ; exact le_pred_of_lt (lt_of_le_of_lt ha hb)
   · exact H
 #align fin.pred_above_right_monotone Fin.predAbove_right_monotone
 
@@ -2499,7 +2499,7 @@ theorem coe_castPred {n : ℕ} (a : Fin (n + 2)) (hx : a < Fin.last _) : (a.cast
   by
   rcases a with ⟨a, ha⟩
   rw [cast_pred_mk]
-  exacts[rfl, hx]
+  exacts [rfl, hx]
 #align fin.coe_cast_pred Fin.coe_castPred
 -/
 
@@ -2545,7 +2545,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
     -- For some reason `simp` doesn't fire fully unless we discharge the third goal.
     · exact lt_of_le_of_ne H (Ne.symm h)
     · simp
-    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSucc_mk] at h
+    · simp only [Fin.mk_eq_mk, Ne.def, Fin.castSucc_mk] at h 
       simp only [pred, Fin.mk_lt_mk, not_lt]
       exact Nat.le_pred_of_lt (Nat.lt_of_le_and_ne H (Ne.symm h))
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
@@ -2610,11 +2610,11 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
       ext
       have h₀ : (b : ℕ) < n + 1 :=
         by
-        simp only [le_iff_coe_le_coe, coe_cast_succ] at h₂
+        simp only [le_iff_coe_le_coe, coe_cast_succ] at h₂ 
         simpa only [lt_succ_iff] using h₂.trans a.is_le
       have h₁ : (b.succ : ℕ) < n + 2 :=
         by
-        rw [← Nat.succ_lt_succ_iff] at h₀
+        rw [← Nat.succ_lt_succ_iff] at h₀ 
         simpa only [coe_succ] using h₀
       simp only [coe_cast_pred b h₀, coe_cast_pred b.succ h₁, coe_succ]
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -248,18 +248,14 @@ theorem mk_val (i : Fin n) : (⟨i, i.property⟩ : Fin n) = i :=
 #align fin.mk_coe Fin.mk_val
 -/
 
-/- warning: fin.coe_eq_val clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align fin.coe_eq_val [anonymous]ₓ'. -/
-theorem [anonymous] (a : Fin n) : (a : ℕ) = a.val :=
+theorem coe_eq_val (a : Fin n) : (a : ℕ) = a.val :=
   rfl
-#align fin.coe_eq_val [anonymous]
+#align fin.coe_eq_val Fin.coe_eq_val
 
-/- warning: fin.val_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align fin.val_eq_coe [anonymous]ₓ'. -/
 @[simp]
-theorem [anonymous] (a : Fin n) : a.val = a :=
+theorem val_eq_coe (a : Fin n) : a.val = a :=
   rfl
-#align fin.val_eq_coe [anonymous]
+#align fin.val_eq_coe Fin.val_eq_coe
 
 #print Fin.heq_fun_iff /-
 /-- Assume `k = l`. If two functions defined on `fin k` and `fin l` are equal on each element,

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -672,16 +672,20 @@ theorem coe_orderIso_apply (e : Fin n ≃o Fin m) (i : Fin n) : (e i : ℕ) = i
   · rwa [← h j hj (hj.trans hi), ← lt_iff_coe_lt_coe, e.lt_iff_lt]
 #align fin.coe_order_iso_apply Fin.coe_orderIso_apply
 
+#print Fin.orderIso_subsingleton /-
 instance orderIso_subsingleton : Subsingleton (Fin n ≃o α) :=
   ⟨fun e e' => by
     ext i
     rw [← e.symm.apply_eq_iff_eq, e.symm_apply_apply, ← e'.trans_apply, ext_iff,
       coe_order_iso_apply]⟩
 #align fin.order_iso_subsingleton Fin.orderIso_subsingleton
+-/
 
+#print Fin.orderIso_subsingleton' /-
 instance orderIso_subsingleton' : Subsingleton (α ≃o Fin n) :=
   OrderIso.symm_injective.Subsingleton
 #align fin.order_iso_subsingleton' Fin.orderIso_subsingleton'
+-/
 
 #print Fin.orderIsoUnique /-
 instance orderIsoUnique : Unique (Fin n ≃o Fin n) :=
@@ -1727,11 +1731,13 @@ theorem coe_subNat (i : Fin (n + m)) (h : m ≤ i) : (i.subNat m h : ℕ) = i -
 #align fin.coe_sub_nat Fin.coe_subNat
 -/
 
+#print Fin.subNat_mk /-
 @[simp]
 theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
     subNat m ⟨i, h₁⟩ h₂ = ⟨i - m, (tsub_lt_iff_right h₂).2 h₁⟩ :=
   rfl
 #align fin.sub_nat_mk Fin.subNat_mk
+-/
 
 @[simp]
 theorem pred_castSucc_succ (i : Fin n) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -106,12 +106,6 @@ def elim0' {α : Sort _} (x : Fin 0) : α :=
 
 variable {n m : ℕ} {a b : Fin n}
 
-/- warning: fin.fin_to_nat -> Fin.coeToNat is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), Coe.{1, 1} (Fin n) Nat
-but is expected to have type
-  forall {n : Nat}, CoeOut.{1, 1} (Fin n) Nat
-Case conversion may be inaccurate. Consider using '#align fin.fin_to_nat Fin.coeToNatₓ'. -/
 instance coeToNat (n : ℕ) : Coe (Fin n) Nat :=
   ⟨Fin.val⟩
 #align fin.fin_to_nat Fin.coeToNat
@@ -255,22 +249,12 @@ theorem mk_val (i : Fin n) : (⟨i, i.property⟩ : Fin n) = i :=
 -/
 
 /- warning: fin.coe_eq_val clashes with [anonymous] -> [anonymous]
-warning: fin.coe_eq_val -> [anonymous] is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {n : Type.{u}} {a : Type.{v}}, (Nat -> n -> a) -> Nat -> (List.{u} n) -> (List.{v} a)
 Case conversion may be inaccurate. Consider using '#align fin.coe_eq_val [anonymous]ₓ'. -/
 theorem [anonymous] (a : Fin n) : (a : ℕ) = a.val :=
   rfl
 #align fin.coe_eq_val [anonymous]
 
 /- warning: fin.val_eq_coe clashes with [anonymous] -> [anonymous]
-warning: fin.val_eq_coe -> [anonymous] is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {n : Type.{u}} {a : Type.{v}}, (Nat -> n -> a) -> Nat -> (List.{u} n) -> (List.{v} a)
 Case conversion may be inaccurate. Consider using '#align fin.val_eq_coe [anonymous]ₓ'. -/
 @[simp]
 theorem [anonymous] (a : Fin n) : a.val = a :=
@@ -385,34 +369,16 @@ theorem mk_lt_mk {x y : Nat} {hx} {hy} : (⟨x, hx⟩ : Fin n) < ⟨y, hy⟩ ↔
 #align fin.mk_lt_mk Fin.mk_lt_mk
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align fin.min_coe Fin.min_valₓ'. -/
 @[simp]
 theorem min_val : min (a : ℕ) n = a := by simp
 #align fin.min_coe Fin.min_val
 
-/- warning: fin.max_coe -> Fin.max_val is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align fin.max_coe Fin.max_valₓ'. -/
 @[simp]
 theorem max_val : max (a : ℕ) n = n := by simp
 #align fin.max_coe Fin.max_val
 
 instance {n : ℕ} : PartialOrder (Fin n) := by infer_instance
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align fin.coe_strict_mono Fin.val_strictMonoₓ'. -/
 theorem val_strictMono : StrictMono (coe : Fin n → ℕ) := fun _ _ => id
 #align fin.coe_strict_mono Fin.val_strictMono
 
@@ -481,12 +447,6 @@ instance hasOneOfNeZero [NeZero n] : One (Fin n) :=
   ⟨ofNat'' 1⟩
 #align fin.has_one_of_ne_zero Fin.hasOneOfNeZero
 
-/- warning: fin.coe_zero -> Fin.val_zero is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align fin.coe_zero Fin.val_zeroₓ'. -/
 @[simp]
 theorem val_zero (n : ℕ) [NeZero n] : ((0 : Fin n) : ℕ) = 0 :=
   rfl
@@ -495,76 +455,35 @@ theorem val_zero (n : ℕ) [NeZero n] : ((0 : Fin n) : ℕ) = 0 :=
 attribute [simp] val_zero
 
 /- warning: fin.val_zero' clashes with fin.coe_zero -> Fin.val_zero
-warning: fin.val_zero' -> Fin.val_zero is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.val_zero' Fin.val_zeroₓ'. -/
 @[simp]
 theorem val_zero (n) [NeZero n] : (0 : Fin n).val = 0 :=
   rfl
 #align fin.val_zero' Fin.val_zero
 
-/- warning: fin.mk_zero -> Fin.mk_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align fin.mk_zero Fin.mk_zeroₓ'. -/
 @[simp]
 theorem mk_zero [NeZero n] : (⟨0, Nat.pos_of_ne_zero (NeZero.ne n)⟩ : Fin n) = (0 : Fin _) :=
   rfl
 #align fin.mk_zero Fin.mk_zero
 
-/- warning: fin.zero_le -> Fin.zero_le is a dubious translation:
-lean 3 declaration is
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 @[simp]
 theorem zero_le [NeZero n] (a : Fin n) : 0 ≤ a :=
   zero_le a.1
 #align fin.zero_le Fin.zero_le
 
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 theorem zero_lt_one : (0 : Fin (n + 2)) < 1 :=
   Nat.zero_lt_one
 #align fin.zero_lt_one Fin.zero_lt_one
 
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 @[simp]
 theorem not_lt_zero (a : Fin n.succ) : ¬a < 0 :=
   fun.
 #align fin.not_lt_zero Fin.not_lt_zero
 
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 theorem pos_iff_ne_zero [NeZero n] (a : Fin n) : 0 < a ↔ a ≠ 0 := by
   rw [← coe_fin_lt, coe_zero, pos_iff_ne_zero, Ne.def, Ne.def, ext_iff, coe_zero]
 #align fin.pos_iff_ne_zero Fin.pos_iff_ne_zero
 
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 theorem eq_zero_or_eq_succ {n : ℕ} (i : Fin (n + 1)) : i = 0 ∨ ∃ j : Fin n, i = j.succ :=
   by
   rcases i with ⟨_ | j, h⟩
@@ -572,12 +491,6 @@ theorem eq_zero_or_eq_succ {n : ℕ} (i : Fin (n + 1)) : i = 0 ∨ ∃ j : Fin n
   · right; exact ⟨⟨j, Nat.lt_of_succ_lt_succ h⟩, rfl⟩
 #align fin.eq_zero_or_eq_succ Fin.eq_zero_or_eq_succ
 
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 theorem eq_succ_of_ne_zero {n : ℕ} {i : Fin (n + 1)} (hi : i ≠ 0) : ∃ j : Fin n, i = j.succ :=
   (eq_zero_or_eq_succ i).resolve_left hi
 #align fin.eq_succ_of_ne_zero Fin.eq_succ_of_ne_zero
@@ -592,12 +505,6 @@ def rev : Equiv.Perm (Fin n) :=
 #align fin.rev Fin.rev
 -/
 
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 @[simp]
 theorem val_rev (i : Fin n) : (i.rev : ℕ) = n - (i + 1) :=
   rfl
@@ -684,12 +591,6 @@ def revOrderIso {n} : (Fin n)ᵒᵈ ≃o Fin n :=
 #align fin.rev_order_iso Fin.revOrderIso
 -/
 
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 @[simp]
 theorem revOrderIso_symm_apply (i : Fin n) : revOrderIso.symm i = OrderDual.toDual i.rev :=
   rfl
@@ -732,12 +633,6 @@ instance : BoundedOrder (Fin (n + 1)) where
 instance : Lattice (Fin (n + 1)) :=
   LinearOrder.toLattice
 
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 theorem last_pos : (0 : Fin (n + 2)) < last (n + 1) := by simp [lt_iff_coe_lt_coe]
 #align fin.last_pos Fin.last_pos
 
@@ -747,22 +642,10 @@ theorem eq_last_of_not_lt {i : Fin (n + 1)} (h : ¬(i : ℕ) < n) : i = last n :
 #align fin.eq_last_of_not_lt Fin.eq_last_of_not_lt
 -/
 
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 theorem top_eq_last (n : ℕ) : ⊤ = Fin.last n :=
   rfl
 #align fin.top_eq_last Fin.top_eq_last
 
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 theorem bot_eq_zero (n : ℕ) : ⊥ = (0 : Fin (n + 1)) :=
   rfl
 #align fin.bot_eq_zero Fin.bot_eq_zero
@@ -773,12 +656,6 @@ variable {α : Type _} [Preorder α]
 
 open Set
 
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 /-- If `e` is an `order_iso` between `fin n` and `fin m`, then `n = m` and `e` is the identity
 map. In this lemma we state that for each `i : fin n` we have `(e i : ℕ) = (i : ℕ)`. -/
 @[simp]
@@ -795,12 +672,6 @@ theorem coe_orderIso_apply (e : Fin n ≃o Fin m) (i : Fin n) : (e i : ℕ) = i
   · rwa [← h j hj (hj.trans hi), ← lt_iff_coe_lt_coe, e.lt_iff_lt]
 #align fin.coe_order_iso_apply Fin.coe_orderIso_apply
 
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 instance orderIso_subsingleton : Subsingleton (Fin n ≃o α) :=
   ⟨fun e e' => by
     ext i
@@ -808,12 +679,6 @@ instance orderIso_subsingleton : Subsingleton (Fin n ≃o α) :=
       coe_order_iso_apply]⟩
 #align fin.order_iso_subsingleton Fin.orderIso_subsingleton
 
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 instance orderIso_subsingleton' : Subsingleton (α ≃o Fin n) :=
   OrderIso.symm_injective.Subsingleton
 #align fin.order_iso_subsingleton' Fin.orderIso_subsingleton'
@@ -824,12 +689,6 @@ instance orderIsoUnique : Unique (Fin n ≃o Fin n) :=
 #align fin.order_iso_unique Fin.orderIsoUnique
 -/
 
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 /-- Two strictly monotone functions from `fin n` are equal provided that their ranges
 are equal. -/
 theorem strictMono_unique {f g : Fin n → α} (hf : StrictMono f) (hg : StrictMono g)
@@ -838,12 +697,6 @@ theorem strictMono_unique {f g : Fin n → α} (hf : StrictMono f) (hg : StrictM
   congr_arg (Function.comp (coe : range g → α)) (funext <| RelIso.ext_iff.1 this)
 #align fin.strict_mono_unique Fin.strictMono_unique
 
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 /-- Two order embeddings of `fin n` are equal provided that their ranges are equal. -/
 theorem orderEmbedding_eq {f g : Fin n ↪o α} (h : range f = range g) : f = g :=
   RelEmbedding.ext <| funext_iff.1 <| strictMono_unique f.StrictMono g.StrictMono h
@@ -912,23 +765,11 @@ theorem subsingleton_iff_le_one : Subsingleton (Fin n) ↔ n ≤ 1 := by
 
 section Monoid
 
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 @[simp]
 protected theorem add_zero [NeZero n] (k : Fin n) : k + 0 = k := by
   simp [eq_iff_veq, add_def, mod_eq_of_lt (is_lt k)]
 #align fin.add_zero Fin.add_zero
 
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 @[simp]
 protected theorem zero_add [NeZero n] (k : Fin n) : (0 : Fin n) + k = k := by
   simp [eq_iff_veq, add_def, mod_eq_of_lt (is_lt k)]
@@ -969,12 +810,6 @@ theorem val_add {n : ℕ} : ∀ a b : Fin n, ((a + b : Fin n) : ℕ) = (a + b) %
 #align fin.coe_add Fin.val_add
 -/
 
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 theorem val_add_eq_ite {n : ℕ} (a b : Fin n) :
     (↑(a + b) : ℕ) = if n ≤ a + b then a + b - n else a + b := by
   rw [Fin.val_add, Nat.add_mod_eq_ite, Nat.mod_eq_of_lt (show ↑a < n from a.2),
@@ -1004,24 +839,12 @@ theorem val_add_one_of_lt {n : ℕ} {i : Fin n.succ} (h : i < last _) : (↑(i +
 #align fin.coe_add_one_of_lt Fin.val_add_one_of_lt
 -/
 
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 @[simp]
 theorem last_add_one : ∀ n, last n + 1 = 0
   | 0 => Subsingleton.elim _ _
   | n + 1 => by ext; rw [coe_add, coe_zero, coe_last, coe_one, Nat.mod_self]
 #align fin.last_add_one Fin.last_add_one
 
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 theorem val_add_one {n : ℕ} (i : Fin (n + 1)) :
     ((i + 1 : Fin (n + 1)) : ℕ) = if i = last _ then 0 else i + 1 :=
   by
@@ -1072,12 +895,6 @@ theorem val_two {n : ℕ} : ((2 : Fin (n + 3)) : ℕ) = 2 :=
 
 section OfNatCoe
 
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 @[simp]
 theorem ofNat_eq_val (n : ℕ) (a : ℕ) : (ofNat a : Fin (n + 1)) = a :=
   rfl
@@ -1088,12 +905,6 @@ theorem ofNat''_eq_coe (n : ℕ) [NeZero n] (a : ℕ) : (ofNat'' a : Fin n) = a
   rfl
 #align fin.of_nat'_eq_coe Fin.ofNat''ₓ_eq_coe
 
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 /-- Converting an in-range number to `fin n` produces a result
 whose value is the original number.  -/
 theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : (a : Fin n).val = a :=
@@ -1102,12 +913,6 @@ theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : (a : Fin n).
   exact Nat.mod_eq_of_lt h
 #align fin.coe_val_of_lt Fin.val_cast_of_lt
 
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 /-- Converting the value of a `fin n` to `fin n` results
 in the same value.  -/
 theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a :=
@@ -1117,11 +922,6 @@ theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a
 #align fin.coe_val_eq_self Fin.cast_val_eq_self
 
 /- warning: fin.coe_coe_of_lt clashes with fin.coe_val_of_lt -> Fin.val_cast_of_lt
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 Case conversion may be inaccurate. Consider using '#align fin.coe_coe_of_lt Fin.val_cast_of_ltₓ'. -/
 /-- Coercing an in-range number to `fin n`, and converting back
 to `ℕ`, results in that number. -/
@@ -1130,11 +930,6 @@ theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : ((a : Fin n)
 #align fin.coe_coe_of_lt Fin.val_cast_of_lt
 
 /- warning: fin.coe_coe_eq_self clashes with fin.coe_val_eq_self -> Fin.cast_val_eq_self
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 Case conversion may be inaccurate. Consider using '#align fin.coe_coe_eq_self Fin.cast_val_eq_selfₓ'. -/
 /-- Converting a `fin n` to `ℕ` and back results in the same
 value. -/
@@ -1143,33 +938,15 @@ theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : ((a : ℕ) : Fin n)
   cast_val_eq_self a
 #align fin.coe_coe_eq_self Fin.cast_val_eq_self
 
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 theorem cast_nat_eq_last (n) : (n : Fin (n + 1)) = Fin.last n := by
   rw [← Fin.ofNat_eq_val, Fin.ofNat, Fin.last]; simp only [Nat.mod_eq_of_lt n.lt_succ_self]
 #align fin.coe_nat_eq_last Fin.cast_nat_eq_last
 
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 theorem le_val_last (i : Fin (n + 1)) : i ≤ n := by rw [Fin.cast_nat_eq_last]; exact Fin.le_last i
 #align fin.le_coe_last Fin.le_val_last
 
 end OfNatCoe
 
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 theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) < i + 1 :=
   by
   cases n
@@ -1179,32 +956,14 @@ theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) <
     exact Nat.zero_lt_succ _
 #align fin.add_one_pos Fin.add_one_pos
 
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 theorem one_pos : (0 : Fin (n + 2)) < 1 :=
   succ_pos 0
 #align fin.one_pos Fin.one_pos
 
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 theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 :=
   ne_of_lt one_pos
 #align fin.zero_ne_one Fin.zero_ne_one
 
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 @[simp]
 theorem zero_eq_one_iff [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 :=
   by
@@ -1216,12 +975,6 @@ theorem zero_eq_one_iff [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 :=
   · rintro rfl; rfl
 #align fin.zero_eq_one_iff Fin.zero_eq_one_iff
 
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 @[simp]
 theorem one_eq_zero_iff [NeZero n] : (1 : Fin n) = 0 ↔ n = 1 := by rw [eq_comm, zero_eq_one_iff]
 #align fin.one_eq_zero_iff Fin.one_eq_zero_iff
@@ -1241,33 +994,15 @@ theorem val_succ (j : Fin n) : (j.succ : ℕ) = j + 1 := by cases j <;> simp [Fi
 #align fin.coe_succ Fin.val_succ
 -/
 
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 @[simp]
 theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by simp [lt_iff_coe_lt_coe]
 #align fin.succ_pos Fin.succ_pos
 
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 /-- `fin.succ` as an `order_embedding` -/
 def succEmbedding (n : ℕ) : Fin n ↪o Fin (n + 1) :=
   OrderEmbedding.ofStrictMono Fin.succ fun ⟨i, hi⟩ ⟨j, hj⟩ h => succ_lt_succ h
 #align fin.succ_embedding Fin.succEmbedding
 
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 @[simp]
 theorem val_succEmbedding : ⇑(succEmbedding n) = Fin.succ :=
   rfl
@@ -1300,22 +1035,10 @@ theorem succ_inj {a b : Fin n} : a.succ = b.succ ↔ a = b :=
 #align fin.succ_inj Fin.succ_inj
 -/
 
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 theorem succ_ne_zero {n} : ∀ k : Fin n, Fin.succ k ≠ 0
   | ⟨k, hk⟩, HEq => Nat.succ_ne_zero k <| ext_iff.1 HEq
 #align fin.succ_ne_zero Fin.succ_ne_zero
 
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 @[simp]
 theorem succ_zero_eq_one [NeZero n] : Fin.succ (0 : Fin n) = 1 :=
   by
@@ -1324,12 +1047,6 @@ theorem succ_zero_eq_one [NeZero n] : Fin.succ (0 : Fin n) = 1 :=
   · rfl
 #align fin.succ_zero_eq_one Fin.succ_zero_eq_one
 
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 /-- Version of `succ_zero_eq_one` to be used by `dsimp` -/
 @[simp]
 theorem succ_zero_eq_one' : Fin.succ (0 : Fin (n + 1)) = 1 :=
@@ -1361,12 +1078,6 @@ theorem succ_mk (n i : ℕ) (h : i < n) : Fin.succ ⟨i, h⟩ = ⟨i + 1, Nat.su
 #align fin.succ_mk Fin.succ_mk
 -/
 
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 theorem mk_succ_pos (i : ℕ) (h : i < n) : (0 : Fin (n + 1)) < ⟨i.succ, add_lt_add_right h 1⟩ := by
   rw [lt_iff_coe_lt_coe, coe_zero]; exact Nat.succ_pos i
 #align fin.mk_succ_pos Fin.mk_succ_pos
@@ -1421,12 +1132,6 @@ theorem lt_add_one_iff {n : ℕ} {k : Fin (n + 1)} : k < k + 1 ↔ k < last n :=
 #align fin.lt_add_one_iff Fin.lt_add_one_iff
 -/
 
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 @[simp]
 theorem le_zero_iff {n : ℕ} [NeZero n] {k : Fin n} : k ≤ 0 ↔ k = 0 :=
   ⟨fun h => Fin.eq_of_veq <| by rw [Nat.eq_zero_of_le_zero h] <;> rfl, by rintro rfl <;> rfl⟩
@@ -1466,53 +1171,26 @@ def castLE (h : n ≤ m) : Fin n ↪o Fin m :=
 #align fin.cast_le Fin.castLE
 -/
 
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 @[simp]
 theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
   rfl
 #align fin.coe_cast_le Fin.coe_castLE
 
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 @[simp]
 theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
     castLE h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h⟩ :=
   rfl
 #align fin.cast_le_mk Fin.castLE_mk
 
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 @[simp]
 theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [eq_iff_veq]
 #align fin.cast_le_zero Fin.castLE_zero
 
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-Case conversion may be inaccurate. Consider using '#align fin.range_cast_le Fin.range_castLEₓ'. -/
 @[simp]
 theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i : ℕ) < n } :=
   Set.ext fun x => ⟨fun ⟨y, hy⟩ => hy ▸ y.2, fun hx => ⟨⟨x, hx⟩, Fin.ext rfl⟩⟩
 #align fin.range_cast_le Fin.range_castLE
 
-/- warning: fin.coe_of_injective_cast_le_symm -> Fin.coe_of_injective_castLE_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
     ((Equiv.ofInjective _ (castLE h).Injective).symm ⟨i, hi⟩ : ℕ) = i :=
@@ -1521,32 +1199,17 @@ theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi)
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
 #align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symm
 
-/- warning: fin.cast_le_succ -> Fin.castLE_succ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.cast_le_succ Fin.castLE_succₓ'. -/
 @[simp]
 theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
     castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.eq_iff_veq]
 #align fin.cast_le_succ Fin.castLE_succ
 
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 @[simp]
 theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
     Fin.castLE mn (Fin.castLE km i) = Fin.castLE (km.trans mn) i :=
   Fin.ext (by simp only [coe_cast_le])
 #align fin.cast_le_cast_le Fin.castLE_castLE
 
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-Case conversion may be inaccurate. Consider using '#align fin.cast_le_comp_cast_le Fin.castLE_comp_castLEₓ'. -/
 @[simp]
 theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
     Fin.castLE mn ∘ Fin.castLE km = Fin.castLE (km.trans mn) :=
@@ -1569,12 +1232,6 @@ theorem symm_cast (h : n = m) : (cast h).symm = cast h.symm :=
 #align fin.symm_cast Fin.symm_cast
 -/
 
-/- warning: fin.coe_cast -> Fin.coe_cast is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align fin.coe_cast Fin.coe_castₓ'. -/
 /-- While `fin.coe_order_iso_apply` is a more general case of this, we mark this `simp` anyway
 as it is eligible for `dsimp`. -/
 @[simp]
@@ -1582,12 +1239,6 @@ theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : ℕ) = i :=
   rfl
 #align fin.coe_cast Fin.coe_cast
 
-/- warning: fin.cast_zero -> Fin.cast_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align fin.cast_zero Fin.cast_zeroₓ'. -/
 @[simp]
 theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
     cast h (0 : Fin n) =
@@ -1596,31 +1247,16 @@ theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
   ext rfl
 #align fin.cast_zero Fin.cast_zero
 
-/- warning: fin.cast_last -> Fin.cast_last is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.cast_last Fin.cast_lastₓ'. -/
 @[simp]
 theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
   ext (by rw [coe_cast, coe_last, coe_last, Nat.succ_injective h])
 #align fin.cast_last Fin.cast_last
 
-/- warning: fin.cast_mk -> Fin.cast_mk is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align fin.cast_mk Fin.cast_mkₓ'. -/
 @[simp]
 theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h.le⟩ :=
   rfl
 #align fin.cast_mk Fin.cast_mk
 
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(Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n k (Eq.trans.{1} Nat n m k h h')) i)
-Case conversion may be inaccurate. Consider using '#align fin.cast_trans Fin.cast_transₓ'. -/
 @[simp]
 theorem cast_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
     cast h' (cast h i) = cast (Eq.trans h h') i :=
@@ -1633,12 +1269,6 @@ theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) := by ext;
 #align fin.cast_refl Fin.cast_refl
 -/
 
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-Case conversion may be inaccurate. Consider using '#align fin.cast_le_of_eq Fin.castLE_of_eqₓ'. -/
 theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
     (castLE h' : Fin m → Fin n) = Fin.cast h :=
   funext fun _ => rfl
@@ -1651,12 +1281,6 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 #align fin.cast_to_equiv Fin.cast_to_equiv
 -/
 
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-Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
 theorem cast_eq_cast (h : n = m) : (cast h : Fin n → Fin m) = cast (h ▸ rfl) := by subst h; ext;
@@ -1670,111 +1294,57 @@ def castAdd (m) : Fin n ↪o Fin (n + m) :=
 #align fin.cast_add Fin.castAdd
 -/
 
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 @[simp]
 theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
   rfl
 #align fin.coe_cast_add Fin.coe_castAdd
 
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 @[simp]
 theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = cast rfl :=
   rfl
 #align fin.cast_add_zero Fin.castAdd_zero
 
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 theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAdd n i : ℕ) < m :=
   i.2
 #align fin.cast_add_lt Fin.castAdd_lt
 
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 @[simp]
 theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i, lt_add_right i n m h⟩ :=
   rfl
 #align fin.cast_add_mk Fin.castAdd_mk
 
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 @[simp]
 theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m (castLT i hi) = i :=
   ext rfl
 #align fin.cast_add_cast_lt Fin.castAdd_castLT
 
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 @[simp]
 theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt m i) = i :=
   ext rfl
 #align fin.cast_lt_cast_add Fin.castLT_castAdd
 
-/- warning: fin.cast_add_cast -> Fin.castAdd_cast is a dubious translation:
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 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
     castAdd m (Fin.cast h i) = Fin.cast (congr_arg _ h) (castAdd m i) :=
   ext rfl
 #align fin.cast_add_cast Fin.castAdd_cast
 
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 theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (castAdd m i) = castAdd m (cast (add_right_cancel h) i) :=
   ext rfl
 #align fin.cast_cast_add_left Fin.cast_castAdd_left
 
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 @[simp]
 theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
     cast h (castAdd m' i) = castAdd m i :=
   ext rfl
 #align fin.cast_cast_add_right Fin.cast_castAdd_right
 
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 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
     castAdd p (castAdd n i) = cast (add_assoc _ _ _).symm (castAdd (n + p) i) :=
   ext rfl
 #align fin.cast_add_cast_add Fin.castAdd_castAdd
 
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 /-- The cast of the successor is the succesor of the cast. See `fin.succ_cast_eq` for rewriting in
 the reverse direction. -/
 @[simp]
@@ -1783,12 +1353,6 @@ theorem cast_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
   ext <| by simp
 #align fin.cast_succ_eq Fin.cast_succ_eq
 
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 theorem succ_cast_eq {n' : ℕ} (i : Fin n) (h : n = n') :
     (cast h i).succ = cast (by rw [h]) i.succ :=
   ext <| by simp
@@ -1801,63 +1365,30 @@ def castSucc : Fin n ↪o Fin (n + 1) :=
 #align fin.cast_succ Fin.castSucc
 -/
 
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 @[simp]
 theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
   rfl
 #align fin.coe_cast_succ Fin.coe_castSucc
 
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 @[simp]
 theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
   rfl
 #align fin.cast_succ_mk Fin.castSucc_mk
 
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 @[simp]
 theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
     cast h (castSucc i) = castSucc (cast (Nat.succ_injective h) i) := by ext;
   simp only [coe_cast, coe_cast_succ]
 #align fin.cast_cast_succ Fin.cast_castSucc
 
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 theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
   lt_iff_val_lt_val.2 <| by simp only [coe_cast_succ, coe_succ, Nat.lt_succ_self]
 #align fin.cast_succ_lt_succ Fin.castSucc_lt_succ
 
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 theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
   simpa [lt_iff_coe_lt_coe, le_iff_coe_le_coe] using nat.succ_le_succ_iff.symm
 #align fin.le_cast_succ_iff Fin.le_castSucc_iff
 
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 theorem castSucc_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
     i.cast_succ < j ↔ i.succ ≤ j := by
   simpa only [Fin.lt_iff_val_lt_val, Fin.le_iff_val_le_val, Fin.val_succ, Fin.coe_castSucc] using
@@ -1878,133 +1409,61 @@ theorem succ_eq_last_succ {n : ℕ} (i : Fin n.succ) : i.succ = last (n + 1) ↔
 #align fin.succ_eq_last_succ Fin.succ_eq_last_succ
 -/
 
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 @[simp]
 theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT i h) = i :=
   Fin.eq_of_veq rfl
 #align fin.cast_succ_cast_lt Fin.castSucc_castLT
 
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 @[simp]
 theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSucc a) h = a := by
   cases a <;> rfl
 #align fin.cast_lt_cast_succ Fin.castLT_castSucc
 
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 @[simp]
 theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
   (@castSucc n).lt_iff_lt
 #align fin.cast_succ_lt_cast_succ_iff Fin.castSucc_lt_castSucc_iff
 
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 theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
   (castSucc : Fin n ↪o _).Injective
 #align fin.cast_succ_injective Fin.castSucc_injective
 
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 theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
   (castSucc_injective n).eq_iff
 #align fin.cast_succ_inj Fin.castSucc_inj
 
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 theorem castSucc_lt_last (a : Fin n) : castSucc a < last n :=
   lt_iff_val_lt_val.mpr a.is_lt
 #align fin.cast_succ_lt_last Fin.castSucc_lt_last
 
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 @[simp]
 theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
   rfl
 #align fin.cast_succ_zero Fin.castSucc_zero
 
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 @[simp]
 theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
   rfl
 #align fin.cast_succ_one Fin.castSucc_one
 
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 /-- `cast_succ i` is positive when `i` is positive -/
 theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
   simpa [lt_iff_coe_lt_coe] using h
 #align fin.cast_succ_pos Fin.castSucc_pos
 
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 @[simp]
 theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
   Fin.ext_iff.trans <| (Fin.ext_iff.trans <| Iff.rfl).symm
 #align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iff
 
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 theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
   not_iff_not.mpr <| castSucc_eq_zero_iff a
 #align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iff
 
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 theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.succ (castSucc j) := by
   simp [Fin.ext_iff]
 #align fin.cast_succ_fin_succ Fin.castSucc_fin_succ
 
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 @[norm_cast, simp]
 theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
   by
@@ -2012,12 +1471,6 @@ theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
   exact coe_val_of_lt (Nat.lt.step a.is_lt)
 #align fin.coe_eq_cast_succ Fin.coe_eq_castSucc
 
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 @[simp]
 theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
   by
@@ -2026,30 +1479,15 @@ theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
   · simp [a.is_lt, eq_iff_veq, add_def, Nat.mod_eq_of_lt]
 #align fin.coe_succ_eq_succ Fin.coeSucc_eq_succ
 
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 theorem lt_succ : a.cast_succ < a.succ := by
   rw [cast_succ, lt_iff_coe_lt_coe, coe_cast_add, coe_succ]; exact lt_add_one a.val
 #align fin.lt_succ Fin.lt_succ
 
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 @[simp]
 theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = { i | (i : ℕ) < n } :=
   range_castLE _
 #align fin.range_cast_succ Fin.range_castSucc
 
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 @[simp]
 theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
     ((Equiv.ofInjective castSucc (castSucc_injective _)).symm ⟨i, hi⟩ : ℕ) = i :=
@@ -2058,9 +1496,6 @@ theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
 #align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symm
 
-/- warning: fin.succ_cast_succ -> Fin.succ_castSucc is a dubious translation:
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 theorem succ_castSucc {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
   Fin.ext (by simp)
 #align fin.succ_cast_succ Fin.succ_castSucc
@@ -2073,77 +1508,41 @@ def addNat (m) : Fin n ↪o Fin (n + m) :=
 #align fin.add_nat Fin.addNat
 -/
 
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 @[simp]
 theorem coe_addNat (m : ℕ) (i : Fin n) : (addNat m i : ℕ) = i + m :=
   rfl
 #align fin.coe_add_nat Fin.coe_addNat
 
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 @[simp]
 theorem addNat_one {i : Fin n} : addNat 1 i = i.succ := by ext; rw [coe_add_nat, coe_succ]
 #align fin.add_nat_one Fin.addNat_one
 
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 theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNat m i :=
   Nat.le_add_left _ _
 #align fin.le_coe_add_nat Fin.le_coe_addNat
 
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 @[simp]
 theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, add_lt_add_right hi n⟩ :=
   rfl
 #align fin.add_nat_mk Fin.addNat_mk
 
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 @[simp]
 theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
     cast h (addNat 0 i) = cast ((add_zero _).symm.trans h) i :=
   ext <| add_zero _
 #align fin.cast_add_nat_zero Fin.cast_addNat_zero
 
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 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
     addNat m (cast h i) = cast (congr_arg _ h) (addNat m i) :=
   ext rfl
 #align fin.add_nat_cast Fin.addNat_cast
 
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 theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (addNat m i) = addNat m (cast (add_right_cancel h) i) :=
   ext rfl
 #align fin.cast_add_nat_left Fin.cast_addNat_left
 
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 @[simp]
 theorem cast_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
     cast h (addNat m' i) = addNat m i :=
@@ -2158,134 +1557,77 @@ def natAdd (n) {m} : Fin m ↪o Fin (n + m) :=
 #align fin.nat_add Fin.natAdd
 -/
 
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 @[simp]
 theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAdd n i : ℕ) = n + i :=
   rfl
 #align fin.coe_nat_add Fin.coe_natAdd
 
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 @[simp]
 theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAdd n ⟨i, hi⟩ = ⟨n + i, add_lt_add_left hi n⟩ :=
   rfl
 #align fin.nat_add_mk Fin.natAdd_mk
 
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 theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAdd m i :=
   Nat.le_add_right _ _
 #align fin.le_coe_nat_add Fin.le_coe_natAdd
 
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 theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRelEmbedding := by ext;
   apply zero_add
 #align fin.nat_add_zero Fin.natAdd_zero
 
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 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
 theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
     natAdd m (cast h i) = cast (congr_arg _ h) (natAdd m i) :=
   ext rfl
 #align fin.nat_add_cast Fin.natAdd_cast
 
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 theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
     cast h (natAdd m i) = natAdd m (cast (add_left_cancel h) i) :=
   ext rfl
 #align fin.cast_nat_add_right Fin.cast_natAdd_right
 
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 @[simp]
 theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
     cast h (natAdd m' i) = natAdd m i :=
   ext <| (congr_arg (· + (i : ℕ)) (add_right_cancel h) : _)
 #align fin.cast_nat_add_left Fin.cast_natAdd_left
 
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 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     castAdd p (natAdd m i) = cast (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
   ext rfl
 #align fin.cast_add_nat_add Fin.castAdd_natAdd
 
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 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     natAdd m (castAdd p i) = cast (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
   ext rfl
 #align fin.nat_add_cast_add Fin.natAdd_castAdd
 
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 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
     natAdd m (natAdd n i) = cast (add_assoc _ _ _) (natAdd (m + n) i) :=
   ext <| (add_assoc _ _ _).symm
 #align fin.nat_add_nat_add Fin.natAdd_natAdd
 
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 @[simp]
 theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
     cast h (natAdd 0 i) = cast ((zero_add _).symm.trans h) i :=
   ext <| zero_add _
 #align fin.cast_nat_add_zero Fin.cast_natAdd_zero
 
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 @[simp]
 theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAdd n i) = addNat n i :=
   ext <| add_comm _ _
 #align fin.cast_nat_add Fin.cast_natAdd
 
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 @[simp]
 theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNat m i) = natAdd m i :=
   ext <| add_comm _ _
 #align fin.cast_add_nat Fin.cast_addNat
 
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 @[simp]
 theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
   rfl
 #align fin.nat_add_last Fin.natAdd_last
 
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 theorem natAdd_castSucc {m n : ℕ} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
   rfl
 #align fin.nat_add_cast_succ Fin.natAdd_castSucc
@@ -2299,12 +1641,6 @@ section Pred
 -/
 
 
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 @[simp]
 theorem coe_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : ℕ) = j - 1 := by cases j; rfl
 #align fin.coe_pred Fin.coe_pred
@@ -2317,22 +1653,10 @@ theorem succ_pred : ∀ (i : Fin (n + 1)) (h : i ≠ 0), (i.pred h).succ = i
 #align fin.succ_pred Fin.succ_pred
 -/
 
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 @[simp]
 theorem pred_succ (i : Fin n) {h : i.succ ≠ 0} : i.succ.pred h = i := by cases i; rfl
 #align fin.pred_succ Fin.pred_succ
 
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 theorem pred_eq_iff_eq_succ {n : ℕ} (i : Fin (n + 1)) (hi : i ≠ 0) (j : Fin n) :
     i.pred hi = j ↔ i = j.succ :=
   ⟨fun h => by simp only [← h, Fin.succ_pred], fun h => by simp only [h, Fin.pred_succ]⟩
@@ -2356,23 +1680,11 @@ theorem pred_mk {n : ℕ} (i : ℕ) (h : i < n + 1) (w) :
 #align fin.pred_mk Fin.pred_mk
 -/
 
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 @[simp]
 theorem pred_le_pred_iff {n : ℕ} {a b : Fin n.succ} {ha : a ≠ 0} {hb : b ≠ 0} :
     a.pred ha ≤ b.pred hb ↔ a ≤ b := by rw [← succ_le_succ_iff, succ_pred, succ_pred]
 #align fin.pred_le_pred_iff Fin.pred_le_pred_iff
 
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 @[simp]
 theorem pred_lt_pred_iff {n : ℕ} {a b : Fin n.succ} {ha : a ≠ 0} {hb : b ≠ 0} :
     a.pred ha < b.pred hb ↔ a < b := by rw [← succ_lt_succ_iff, succ_pred, succ_pred]
@@ -2387,12 +1699,6 @@ theorem pred_inj : ∀ {a b : Fin (n + 1)} {ha : a ≠ 0} {hb : b ≠ 0}, a.pred
 #align fin.pred_inj Fin.pred_inj
 -/
 
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 @[simp]
 theorem pred_one {n : ℕ} : Fin.pred (1 : Fin (n + 2)) (Ne.symm (ne_of_lt one_pos)) = 0 :=
   rfl
@@ -2421,53 +1727,29 @@ theorem coe_subNat (i : Fin (n + m)) (h : m ≤ i) : (i.subNat m h : ℕ) = i -
 #align fin.coe_sub_nat Fin.coe_subNat
 -/
 
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 @[simp]
 theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
     subNat m ⟨i, h₁⟩ h₂ = ⟨i - m, (tsub_lt_iff_right h₂).2 h₁⟩ :=
   rfl
 #align fin.sub_nat_mk Fin.subNat_mk
 
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 @[simp]
 theorem pred_castSucc_succ (i : Fin n) :
     pred (castSucc i.succ) (ne_of_gt (castSucc_pos i.succ_pos)) = i.cast_succ := by
   simp [eq_iff_veq]
 #align fin.pred_cast_succ_succ Fin.pred_castSucc_succ
 
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 @[simp]
 theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat m (subNat m i h) = i :=
   ext <| tsub_add_cancel_of_le h
 #align fin.add_nat_sub_nat Fin.addNat_subNat
 
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 @[simp]
 theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addNat m i) :
     subNat m (addNat m i) h = i :=
   ext <| add_tsub_cancel_right i m
 #align fin.sub_nat_add_nat Fin.subNat_addNat
 
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 @[simp]
 theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
     natAdd n (subNat n (cast (add_comm _ _) i) h) = i := by simp [← cast_add_nat]
@@ -2514,12 +1796,6 @@ section Rec
 -/
 
 
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 /-- Define `C n i` by induction on `i : fin n` interpreted as `(0 : fin (n - i)).succ.succ…`.
 This function has two arguments: `H0 n` defines `0`-th element `C (n+1) 0` of an `(n+1)`-tuple,
 and `Hs n i` defines `(i+1)`-st element of `(n+1)`-tuple based on `n`, `i`, and `i`-th element
@@ -2532,12 +1808,6 @@ def succRec {C : ∀ n, Fin n → Sort _} (H0 : ∀ n, C (succ n) 0)
   | succ n, ⟨succ i, h⟩ => Hs _ _ (succ_rec ⟨i, lt_of_succ_lt_succ h⟩)
 #align fin.succ_rec Fin.succRec
 
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 /-- Define `C n i` by induction on `i : fin n` interpreted as `(0 : fin (n - i)).succ.succ…`.
 This function has two arguments: `H0 n` defines `0`-th element `C (n+1) 0` of an `(n+1)`-tuple,
 and `Hs n i` defines `(i+1)`-st element of `(n+1)`-tuple based on `n`, `i`, and `i`-th element
@@ -2550,35 +1820,17 @@ def succRecOn {n : ℕ} (i : Fin n) {C : ∀ n, Fin n → Sort _} (H0 : ∀ n, C
   i.succRec H0 Hs
 #align fin.succ_rec_on Fin.succRecOn
 
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 @[simp]
 theorem succRecOn_zero {C : ∀ n, Fin n → Sort _} {H0 Hs} (n) :
     @Fin.succRecOn (succ n) 0 C H0 Hs = H0 n :=
   rfl
 #align fin.succ_rec_on_zero Fin.succRecOn_zero
 
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 @[simp]
 theorem succRecOn_succ {C : ∀ n, Fin n → Sort _} {H0 Hs} {n} (i : Fin n) :
     @Fin.succRecOn (succ n) i.succ C H0 Hs = Hs n i (Fin.succRecOn i H0 Hs) := by cases i <;> rfl
 #align fin.succ_rec_on_succ Fin.succRecOn_succ
 
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 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
 and `hs` defines the inductive step using `C i.cast_succ`.
@@ -2593,33 +1845,18 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
     exact IH (lt_of_succ_lt hi)
 #align fin.induction Fin.induction
 
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 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
     (hs : ∀ i : Fin n, C i.cast_succ → C i.succ) : (induction h0 hs : _) 0 = h0 :=
   rfl
 #align fin.induction_zero Fin.induction_zero
 
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 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
     (hs : ∀ i : Fin n, C i.cast_succ → C i.succ) (i : Fin n) :
     (induction h0 hs : _) i.succ = hs i (induction h0 hs i.cast_succ) := by cases i <;> rfl
 #align fin.induction_succ Fin.induction_succ
 
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 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
 and `hs` defines the inductive step using `C i.cast_succ`.
@@ -2632,12 +1869,6 @@ def inductionOn (i : Fin (n + 1)) {C : Fin (n + 1) → Sort _} (h0 : C 0)
   induction h0 hs i
 #align fin.induction_on Fin.inductionOn
 
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 /-- Define `f : Π i : fin n.succ, C i` by separately handling the cases `i = 0` and
 `i = j.succ`, `j : fin n`. -/
 @[elab_as_elim]
@@ -2646,116 +1877,50 @@ def cases {C : Fin (succ n) → Sort _} (H0 : C 0) (Hs : ∀ i : Fin n, C i.succ
   induction H0 fun i _ => Hs i
 #align fin.cases Fin.cases
 
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 @[simp]
 theorem cases_zero {n} {C : Fin (succ n) → Sort _} {H0 Hs} : @Fin.cases n C H0 Hs 0 = H0 :=
   rfl
 #align fin.cases_zero Fin.cases_zero
 
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 @[simp]
 theorem cases_succ {n} {C : Fin (succ n) → Sort _} {H0 Hs} (i : Fin n) :
     @Fin.cases n C H0 Hs i.succ = Hs i := by cases i <;> rfl
 #align fin.cases_succ Fin.cases_succ
 
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 @[simp]
 theorem cases_succ' {n} {C : Fin (succ n) → Sort _} {H0 Hs} {i : ℕ} (h : i + 1 < n + 1) :
     @Fin.cases n C H0 Hs ⟨i.succ, h⟩ = Hs ⟨i, lt_of_succ_lt_succ h⟩ := by cases i <;> rfl
 #align fin.cases_succ' Fin.cases_succ'
 
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 theorem forall_fin_succ {P : Fin (n + 1) → Prop} : (∀ i, P i) ↔ P 0 ∧ ∀ i : Fin n, P i.succ :=
   ⟨fun H => ⟨H 0, fun i => H _⟩, fun ⟨H0, H1⟩ i => Fin.cases H0 H1 i⟩
 #align fin.forall_fin_succ Fin.forall_fin_succ
 
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 theorem exists_fin_succ {P : Fin (n + 1) → Prop} : (∃ i, P i) ↔ P 0 ∨ ∃ i : Fin n, P i.succ :=
   ⟨fun ⟨i, h⟩ => Fin.cases Or.inl (fun i hi => Or.inr ⟨i, hi⟩) i h, fun h =>
     h.elim (fun h => ⟨0, h⟩) fun ⟨i, hi⟩ => ⟨i.succ, hi⟩⟩
 #align fin.exists_fin_succ Fin.exists_fin_succ
 
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 theorem forall_fin_one {p : Fin 1 → Prop} : (∀ i, p i) ↔ p 0 :=
   @Unique.forall_iff (Fin 1) _ p
 #align fin.forall_fin_one Fin.forall_fin_one
 
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 theorem exists_fin_one {p : Fin 1 → Prop} : (∃ i, p i) ↔ p 0 :=
   @Unique.exists_iff (Fin 1) _ p
 #align fin.exists_fin_one Fin.exists_fin_one
 
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 theorem forall_fin_two {p : Fin 2 → Prop} : (∀ i, p i) ↔ p 0 ∧ p 1 :=
   forall_fin_succ.trans <| and_congr_right fun _ => forall_fin_one
 #align fin.forall_fin_two Fin.forall_fin_two
 
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 theorem exists_fin_two {p : Fin 2 → Prop} : (∃ i, p i) ↔ p 0 ∨ p 1 :=
   exists_fin_succ.trans <| or_congr_right exists_fin_one
 #align fin.exists_fin_two Fin.exists_fin_two
 
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 theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b := by revert a b;
   simp [forall_fin_two]
 #align fin.fin_two_eq_of_eq_zero_iff Fin.fin_two_eq_of_eq_zero_iff
 
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 /--
 Define `C i` by reverse induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `hlast` handles the base case on `C (fin.last n)`,
@@ -2776,12 +1941,6 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
   ⟨_, measure_wf fun i : Fin (n + 1) => n + 1 - i⟩
 #align fin.reverse_induction Fin.reverseInduction
 
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 @[simp]
 theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) :
@@ -2789,9 +1948,6 @@ theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (F
   rw [reverse_induction] <;> simp
 #align fin.reverse_induction_last Fin.reverse_induction_last
 
-/- warning: fin.reverse_induction_cast_succ -> Fin.reverse_induction_castSucc is a dubious translation:
-<too large>
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 @[simp]
 theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
     (hs : ∀ i : Fin n, C i.succ → C i.cast_succ) (i : Fin n) :
@@ -2802,12 +1958,6 @@ theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 :
   rfl
 #align fin.reverse_induction_cast_succ Fin.reverse_induction_castSucc
 
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 /-- Define `f : Π i : fin n.succ, C i` by separately handling the cases `i = fin.last n` and
 `i = j.cast_succ`, `j : fin n`. -/
 @[elab_as_elim]
@@ -2816,12 +1966,6 @@ def lastCases {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
   reverseInduction hlast (fun i _ => hcast i) i
 #align fin.last_cases Fin.lastCases
 
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 @[simp]
 theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) :
@@ -2829,9 +1973,6 @@ theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.la
   reverse_induction_last _ _
 #align fin.last_cases_last Fin.lastCases_last
 
-/- warning: fin.last_cases_cast_succ -> Fin.lastCases_castSucc is a dubious translation:
-<too large>
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 @[simp]
 theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
     (hcast : ∀ i : Fin n, C i.cast_succ) (i : Fin n) :
@@ -2839,12 +1980,6 @@ theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fi
   reverse_induction_castSucc _ _ _
 #align fin.last_cases_cast_succ Fin.lastCases_castSucc
 
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-Case conversion may be inaccurate. Consider using '#align fin.add_cases Fin.addCasesₓ'. -/
 /-- Define `f : Π i : fin (m + n), C i` by separately handling the cases `i = cast_add n i`,
 `j : fin m` and `i = nat_add m j`, `j : fin n`. -/
 @[elab_as_elim]
@@ -2854,9 +1989,6 @@ def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd
   else Eq.recOn (natAdd_subNat_cast (le_of_not_lt hi)) (hright _)
 #align fin.add_cases Fin.addCases
 
-/- warning: fin.add_cases_left -> Fin.addCases_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.add_cases_left Fin.addCases_leftₓ'. -/
 @[simp]
 theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
     (hright : ∀ i, C (natAdd m i)) (i : Fin m) :
@@ -2867,9 +1999,6 @@ theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C
   rfl
 #align fin.add_cases_left Fin.addCases_left
 
-/- warning: fin.add_cases_right -> Fin.addCases_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.add_cases_right Fin.addCases_rightₓ'. -/
 @[simp]
 theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
     (hright : ∀ i, C (natAdd m i)) (i : Fin n) :
@@ -2883,12 +2012,6 @@ theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i,
 
 end Rec
 
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-Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=
   by
@@ -2903,12 +2026,6 @@ theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r]
       exacts[H j, trans (ihj hlt) (H j)]
 #align fin.lift_fun_iff_succ Fin.lift_fun_iff_succ
 
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 /-- A function `f` on `fin (n + 1)` is strictly monotone if and only if `f i < f (i + 1)`
 for all `i`. -/
 theorem strictMono_iff_lt_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
@@ -2916,24 +2033,12 @@ theorem strictMono_iff_lt_succ {α : Type _} [Preorder α] {f : Fin (n + 1) →
   lift_fun_iff_succ (· < ·)
 #align fin.strict_mono_iff_lt_succ Fin.strictMono_iff_lt_succ
 
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 /-- A function `f` on `fin (n + 1)` is monotone if and only if `f i ≤ f (i + 1)` for all `i`. -/
 theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     Monotone f ↔ ∀ i : Fin n, f i.cast_succ ≤ f i.succ :=
   monotone_iff_forall_lt.trans <| lift_fun_iff_succ (· ≤ ·)
 #align fin.monotone_iff_le_succ Fin.monotone_iff_le_succ
 
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 /-- A function `f` on `fin (n + 1)` is strictly antitone if and only if `f (i + 1) < f i`
 for all `i`. -/
 theorem strictAnti_iff_succ_lt {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
@@ -2941,12 +2046,6 @@ theorem strictAnti_iff_succ_lt {α : Type _} [Preorder α] {f : Fin (n + 1) →
   lift_fun_iff_succ (· > ·)
 #align fin.strict_anti_iff_succ_lt Fin.strictAnti_iff_succ_lt
 
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 /-- A function `f` on `fin (n + 1)` is antitone if and only if `f (i + 1) ≤ f i` for all `i`. -/
 theorem antitone_iff_succ_le {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
     Antitone f ↔ ∀ i : Fin n, f i.succ ≤ f i.cast_succ :=
@@ -2974,12 +2073,6 @@ instance (n : ℕ) [NeZero n] : AddCommGroup (Fin n) :=
       Fin.ext <| show (a + (n - b)) % n = (a + (n - b) % n) % n by simp
     sub := Fin.sub }
 
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 protected theorem coe_neg (a : Fin n) : ((-a : Fin n) : ℕ) = (n - a) % n :=
   rfl
 #align fin.coe_neg Fin.coe_neg
@@ -2996,12 +2089,6 @@ theorem coe_fin_one (a : Fin 1) : ↑a = 0 := by rw [Subsingleton.elim a 0, Fin.
 #align fin.coe_fin_one Fin.coe_fin_one
 -/
 
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 @[simp]
 theorem coe_neg_one : ↑(-1 : Fin (n + 1)) = n :=
   by
@@ -3011,12 +2098,6 @@ theorem coe_neg_one : ↑(-1 : Fin (n + 1)) = n :=
   constructor
 #align fin.coe_neg_one Fin.coe_neg_one
 
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-Case conversion may be inaccurate. Consider using '#align fin.coe_sub_one Fin.coe_sub_oneₓ'. -/
 theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a - 1 :=
   by
   cases n
@@ -3056,12 +2137,6 @@ theorem coe_sub_iff_lt {n : ℕ} {a b : Fin n} : (↑(a - b) : ℕ) = n + a - b
 #align fin.coe_sub_iff_lt Fin.coe_sub_iff_lt
 -/
 
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 @[simp]
 theorem lt_sub_one_iff {n : ℕ} {k : Fin (n + 2)} : k < k - 1 ↔ k = 0 :=
   by
@@ -3073,12 +2148,6 @@ theorem lt_sub_one_iff {n : ℕ} {k : Fin (n + 2)} : k < k - 1 ↔ k = 0 :=
     mod_eq_of_lt ((lt_succ_self _).trans hk)]
 #align fin.lt_sub_one_iff Fin.lt_sub_one_iff
 
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 @[simp]
 theorem le_sub_one_iff {n : ℕ} {k : Fin (n + 1)} : k ≤ k - 1 ↔ k = 0 :=
   by
@@ -3089,12 +2158,6 @@ theorem le_sub_one_iff {n : ℕ} {k : Fin (n + 1)} : k ≤ k - 1 ↔ k = 0 :=
   simp
 #align fin.le_sub_one_iff Fin.le_sub_one_iff
 
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 @[simp]
 theorem sub_one_lt_iff {n : ℕ} {k : Fin (n + 1)} : k - 1 < k ↔ 0 < k :=
   not_iff_not.1 <| by simp only [not_lt, le_sub_one_iff, le_zero_iff]
@@ -3110,9 +2173,6 @@ end AddGroup
 
 section SuccAbove
 
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 theorem succAbove_aux (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
   (castSucc : Fin n ↪o _).StrictMono.ite (succEmbedding n).StrictMono
@@ -3120,32 +2180,17 @@ theorem succAbove_aux (p : Fin (n + 1)) :
     (castSucc_lt_succ i).le
 #align fin.succ_above_aux Fin.succAbove_aux
 
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 /-- `succ_above p i` embeds `fin n` into `fin (n + 1)` with a hole around `p`. -/
 def succAbove (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
   OrderEmbedding.ofStrictMono _ p.succAbove_aux
 #align fin.succ_above Fin.succAbove
 
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 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
 theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
     p.succAbove i = i.cast_succ := by rw [succ_above]; exact if_pos h
 #align fin.succ_above_below Fin.succAbove_below
 
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 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 :=
   by
@@ -3154,91 +2199,49 @@ theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.s
   · exact bot_lt_iff_ne_bot.mpr ha
 #align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zero
 
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-Case conversion may be inaccurate. Consider using '#align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iffₓ'. -/
 theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) :
     a.succAbove b = 0 ↔ b = 0 := by
   simp only [← succ_above_ne_zero_zero ha, OrderEmbedding.eq_iff_eq]
 #align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iff
 
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 theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) (hb : b ≠ 0) :
     a.succAbove b ≠ 0 :=
   mt (succAbove_eq_zero_iff ha).mp hb
 #align fin.succ_above_ne_zero Fin.succAbove_ne_zero
 
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 /-- Embedding `fin n` into `fin (n + 1)` with a hole around zero embeds by `succ`. -/
 @[simp]
 theorem succAbove_zero : ⇑(succAbove (0 : Fin (n + 1))) = Fin.succ :=
   rfl
 #align fin.succ_above_zero Fin.succAbove_zero
 
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 /-- Embedding `fin n` into `fin (n + 1)` with a hole around `last n` embeds by `cast_succ`. -/
 @[simp]
 theorem succAbove_last : succAbove (Fin.last n) = castSucc := by ext;
   simp only [succ_above_below, cast_succ_lt_last]
 #align fin.succ_above_last Fin.succAbove_last
 
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 theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_succ := by
   rw [succ_above_last]
 #align fin.succ_above_last_apply Fin.succAbove_last_apply
 
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 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
 theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
     p.succAbove i = i.succ := by simp [succ_above, h.not_lt]
 #align fin.succ_above_above Fin.succAbove_above
 
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 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p ≤ i.cast_succ :=
   lt_or_ge (castSucc i) p
 #align fin.succ_above_lt_ge Fin.succAbove_lt_ge
 
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 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
   Or.cases_on (succAbove_lt_ge p i) (fun h => Or.inl h) fun h =>
     Or.inr (lt_of_le_of_lt h (castSucc_lt_succ i))
 #align fin.succ_above_lt_gt Fin.succAbove_lt_gt
 
-/- warning: fin.succ_above_lt_iff -> Fin.succAbove_lt_iff is a dubious translation:
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 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
 @[simp]
@@ -3255,9 +2258,6 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
     exact h
 #align fin.succ_above_lt_iff Fin.succAbove_lt_iff
 
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 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
 theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p ≤ i.cast_succ :=
@@ -3273,12 +2273,6 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
     exact lt_of_le_of_lt h (cast_succ_lt_succ i)
 #align fin.lt_succ_above_iff Fin.lt_succAbove_iff
 
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 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 never results in `p` itself -/
 theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
@@ -3289,12 +2283,6 @@ theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
   · simpa [← succ_above_above _ _ (le_of_not_lt H), Eq] using cast_succ_lt_succ i
 #align fin.succ_above_ne Fin.succAbove_ne
 
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 /-- Embedding a positive `fin n` results in a positive fin (n + 1)` -/
 theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i :=
   by
@@ -3303,61 +2291,34 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
   · simp [succ_above_above _ _ (le_of_not_lt H)]
 #align fin.succ_above_pos Fin.succAbove_pos
 
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 @[simp]
 theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
     (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLT hx) = x := by
   rw [succ_above_below, cast_succ_cast_lt]; exact h
 #align fin.succ_above_cast_lt Fin.succAbove_castLT
 
-/- warning: fin.succ_above_pred -> Fin.succAbove_pred is a dubious translation:
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 @[simp]
 theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
     x.succAbove (y.pred hy) = y := by rw [succ_above_above, succ_pred];
   simpa [le_iff_coe_le_coe] using Nat.le_pred_of_lt h
 #align fin.succ_above_pred Fin.succAbove_pred
 
-/- warning: fin.cast_lt_succ_above -> Fin.castLT_succAbove is a dubious translation:
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 theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
     (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
     (y.succAbove x).castLT h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
 #align fin.cast_lt_succ_above Fin.castLT_succAbove
 
-/- warning: fin.pred_succ_above -> Fin.pred_succAbove is a dubious translation:
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 theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
     (h' : y.succAbove x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
     (y.succAbove x).pred h' = x := by simp only [succ_above_above _ _ h, pred_succ]
 #align fin.pred_succ_above Fin.pred_succAbove
 
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 theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x :=
   by
   cases' h.lt_or_lt with hlt hlt
   exacts[⟨_, succ_above_cast_lt hlt⟩, ⟨_, succ_above_pred hlt⟩]
 #align fin.exists_succ_above_eq Fin.exists_succAbove_eq
 
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 @[simp]
 theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y) ↔ y ≠ x :=
   by
@@ -3366,107 +2327,53 @@ theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y)
   exact succ_above_ne _ _
 #align fin.exists_succ_above_eq_iff Fin.exists_succAbove_eq_iff
 
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 /-- The range of `p.succ_above` is everything except `p`. -/
 @[simp]
 theorem range_succAbove (p : Fin (n + 1)) : Set.range p.succAbove = {p}ᶜ :=
   Set.ext fun _ => exists_succAbove_eq_iff
 #align fin.range_succ_above Fin.range_succAbove
 
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 @[simp]
 theorem range_succ (n : ℕ) : Set.range (Fin.succ : Fin n → Fin (n + 1)) = {0}ᶜ :=
   range_succAbove 0
 #align fin.range_succ Fin.range_succ
 
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 @[simp]
 theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠ 0 :=
   @exists_succAbove_eq_iff n 0 x
 #align fin.exists_succ_eq_iff Fin.exists_succ_eq_iff
 
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 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
   (succAbove x).Injective
 #align fin.succ_above_right_injective Fin.succAbove_right_injective
 
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 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b ↔ a = b :=
   succAbove_right_injective.eq_iff
 #align fin.succ_above_right_inj Fin.succAbove_right_inj
 
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 /-- `succ_above` is injective at the pivot -/
 theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
   simpa [range_succ_above] using congr_arg (fun f : Fin n ↪o Fin (n + 1) => Set.range fᶜ) h
 #align fin.succ_above_left_injective Fin.succAbove_left_injective
 
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 /-- `succ_above` is injective at the pivot -/
 @[simp]
 theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAbove = y.succAbove ↔ x = y :=
   succAbove_left_injective.eq_iff
 #align fin.succ_above_left_inj Fin.succAbove_left_inj
 
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 @[simp]
 theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i.succ :=
   rfl
 #align fin.zero_succ_above Fin.zero_succAbove
 
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 @[simp]
 theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove 0 = 0 :=
   succAbove_below _ _ (succ_pos _)
 #align fin.succ_succ_above_zero Fin.succ_succAbove_zero
 
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 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
     i.succ.succAbove j.succ = (i.succAbove j).succ :=
@@ -3481,17 +2388,11 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
     simp [succ_above_above _ _ h, succ_above_above _ _ h']
 #align fin.succ_succ_above_succ Fin.succ_succAbove_succ
 
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 @[simp]
 theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
   succ_succAbove_zero 0
 #align fin.one_succ_above_zero Fin.one_succAbove_zero
 
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 /-- By moving `succ` to the outside of this expression, we create opportunities for further
 simplification using `succ_above_zero` or `succ_succ_above_zero`. -/
 @[simp]
@@ -3500,17 +2401,11 @@ theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
   rw [← succ_succ_above_succ i 0, succ_zero_eq_one]
 #align fin.succ_succ_above_one Fin.succ_succAbove_one
 
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 @[simp]
 theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j.succ = j.succ.succ :=
   succ_succAbove_succ 0 j
 #align fin.one_succ_above_succ Fin.one_succAbove_succ
 
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 @[simp]
 theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 :=
   succ_succAbove_succ 0 0
@@ -3528,12 +2423,6 @@ def predAbove (p : Fin n) (i : Fin (n + 1)) : Fin n :=
 #align fin.pred_above Fin.predAbove
 -/
 
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 theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H =>
   by
   dsimp [pred_above]
@@ -3549,12 +2438,6 @@ theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H
   · exact H
 #align fin.pred_above_right_monotone Fin.predAbove_right_monotone
 
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 theorem predAbove_left_monotone (i : Fin (n + 1)) : Monotone fun p => predAbove p i := fun a b H =>
   by
   dsimp [pred_above]
@@ -3573,12 +2456,6 @@ def castPred (i : Fin (n + 2)) : Fin (n + 1) :=
 #align fin.cast_pred Fin.castPred
 -/
 
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 @[simp]
 theorem castPred_zero : castPred (0 : Fin (n + 2)) = 0 :=
   rfl
@@ -3590,12 +2467,6 @@ theorem castPred_one : castPred (1 : Fin (n + 2)) = 1 := by cases n; apply Subsi
 #align fin.cast_pred_one Fin.castPred_one
 -/
 
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 @[simp]
 theorem predAbove_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred hi :=
   by
@@ -3630,9 +2501,6 @@ theorem coe_castPred {n : ℕ} (a : Fin (n + 2)) (hx : a < Fin.last _) : (a.cast
 #align fin.coe_cast_pred Fin.coe_castPred
 -/
 
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-<too large>
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 theorem predAbove_below (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_succ) :
     p.predAbove i = i.cast_pred :=
   by
@@ -3647,36 +2515,18 @@ theorem predAbove_last : predAbove (Fin.last n) = castPred :=
 #align fin.pred_above_last Fin.predAbove_last
 -/
 
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 theorem predAbove_last_apply (i : Fin n) : predAbove (Fin.last n) i = i.cast_pred := by
   rw [pred_above_last]
 #align fin.pred_above_last_apply Fin.predAbove_last_apply
 
-/- warning: fin.pred_above_above -> Fin.predAbove_above is a dubious translation:
-<too large>
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 theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
     p.predAbove i = i.pred (p.cast_succ.zero_le.trans_lt h).Ne.symm := by simp [pred_above, h]
 #align fin.pred_above_above Fin.predAbove_above
 
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-  forall {n : Nat}, Monotone.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.castPred n)
-Case conversion may be inaccurate. Consider using '#align fin.cast_pred_monotone Fin.castPred_monotoneₓ'. -/
 theorem castPred_monotone : Monotone (@castPred n) :=
   predAbove_right_monotone (last _)
 #align fin.cast_pred_monotone Fin.castPred_monotone
 
-/- warning: fin.succ_above_pred_above -> Fin.succAbove_predAbove is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred_above Fin.succAbove_predAboveₓ'. -/
 /-- Sending `fin (n+1)` to `fin n` by subtracting one from anything above `p`
 then back to `fin (n+1)` with a gap around `p` is the identity away from `p`. -/
 @[simp]
@@ -3698,9 +2548,6 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
       exact Nat.le_pred_of_lt (Nat.lt_of_le_and_ne H (Ne.symm h))
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
 
-/- warning: fin.pred_above_succ_above -> Fin.predAbove_succAbove is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.pred_above_succ_above Fin.predAbove_succAboveₓ'. -/
 /-- Sending `fin n` into `fin (n + 1)` with a gap at `p`
 then back to `fin n` by subtracting one from anything above `p` is the identity. -/
 @[simp]
@@ -3721,17 +2568,11 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
       exact lt_succ_iff.mpr (not_lt.mp h)
 #align fin.pred_above_succ_above Fin.predAbove_succAbove
 
-/- warning: fin.cast_succ_pred_eq_pred_cast_succ -> Fin.castSucc_pred_eq_pred_castSucc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSuccₓ'. -/
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
     (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' := by
   cases a; rfl
 #align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSucc
 
-/- warning: fin.pred_succ_above_pred -> Fin.pred_succAbove_pred is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above_pred Fin.pred_succAbove_predₓ'. -/
 /-- `pred` commutes with `succ_above`. -/
 theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
     (hk := succAbove_ne_zero ha hb) : (a.pred ha).succAbove (b.pred hb) = (a.succAbove b).pred hk :=
@@ -3777,17 +2618,11 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ
 -/
 
-/- warning: fin.cast_pred_cast_succ -> Fin.castPred_castSucc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.cast_pred_cast_succ Fin.castPred_castSuccₓ'. -/
 @[simp]
 theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
   simp [cast_pred, pred_above, le_last]
 #align fin.cast_pred_cast_succ Fin.castPred_castSucc
 
-/- warning: fin.cast_succ_cast_pred -> Fin.castSucc_castPred is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_pred Fin.castSucc_castPredₓ'. -/
 theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSucc i.cast_pred = i :=
   by
   rw [cast_pred, pred_above, dif_neg]
@@ -3837,23 +2672,11 @@ def clamp (n m : ℕ) : Fin (m + 1) :=
 #align fin.clamp Fin.clamp
 -/
 
-/- warning: fin.coe_clamp -> Fin.coe_clamp is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat) (m : Nat), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Fin.clamp n m)) (LinearOrder.min.{0} Nat Nat.linearOrder n m)
-but is expected to have type
-  forall (n : Nat) (m : Nat), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.clamp n m)) (Min.min.{0} Nat instMinNat n m)
-Case conversion may be inaccurate. Consider using '#align fin.coe_clamp Fin.coe_clampₓ'. -/
 @[simp]
 theorem coe_clamp (n m : ℕ) : (clamp n m : ℕ) = min n m :=
   Nat.mod_eq_of_lt <| Nat.lt_succ_iff.mpr <| min_le_right _ _
 #align fin.coe_clamp Fin.coe_clamp
 
-/- warning: fin.coe_of_nat_eq_mod -> Fin.coe_ofNat_eq_mod is a dubious translation:
-lean 3 declaration is
-  forall (m : Nat) (n : Nat) [_inst_1 : NeZero.{0} Nat Nat.hasZero m], Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (Fin m) (HasLiftT.mk.{1, 1} Nat (Fin m) (CoeTCₓ.coe.{1, 1} Nat (Fin m) (Nat.castCoe.{0} (Fin m) (AddMonoidWithOne.toNatCast.{0} (Fin m) (Fin.addMonoidWithOne m _inst_1))))) n)) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n m)
-but is expected to have type
-  forall (m : Nat) (n : Nat) [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) m], Eq.{1} Nat (Fin.val m (Nat.cast.{0} (Fin m) (AddMonoidWithOne.toNatCast.{0} (Fin m) (Fin.instAddMonoidWithOneFin m _inst_1)) n)) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n m)
-Case conversion may be inaccurate. Consider using '#align fin.coe_of_nat_eq_mod Fin.coe_ofNat_eq_modₓ'. -/
 @[simp]
 theorem coe_ofNat_eq_mod (m n : ℕ) [NeZero m] : ((n : Fin m) : ℕ) = n % m :=
   rfl
@@ -3903,22 +2726,10 @@ protected theorem one_mul [NeZero n] (k : Fin n) : (1 : Fin n) * k = k := by
 #align fin.one_mul Fin.one_mul
 -/
 
-/- warning: fin.mul_zero -> Fin.mul_zero is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (k : Fin n), Eq.{1} (Fin n) (HMul.hMul.{0, 0, 0} (Fin n) (Fin n) (Fin n) (instHMul.{0} (Fin n) (Fin.hasMul n)) k (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))
-but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (k : Fin n), Eq.{1} (Fin n) (HMul.hMul.{0, 0, 0} (Fin n) (Fin n) (Fin n) (instHMul.{0} (Fin n) (Fin.instMulFin n)) k (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))
-Case conversion may be inaccurate. Consider using '#align fin.mul_zero Fin.mul_zeroₓ'. -/
 @[simp]
 protected theorem mul_zero [NeZero n] (k : Fin n) : k * 0 = 0 := by simp [eq_iff_veq, mul_def]
 #align fin.mul_zero Fin.mul_zero
 
-/- warning: fin.zero_mul -> Fin.zero_mul is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (k : Fin n), Eq.{1} (Fin n) (HMul.hMul.{0, 0, 0} (Fin n) (Fin n) (Fin n) (instHMul.{0} (Fin n) (Fin.hasMul n)) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))) k) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))
-but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (k : Fin n), Eq.{1} (Fin n) (HMul.hMul.{0, 0, 0} (Fin n) (Fin n) (Fin n) (instHMul.{0} (Fin n) (Fin.instMulFin n)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) k) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))
-Case conversion may be inaccurate. Consider using '#align fin.zero_mul Fin.zero_mulₓ'. -/
 @[simp]
 protected theorem zero_mul [NeZero n] (k : Fin n) : (0 : Fin n) * k = 0 := by
   simp [eq_iff_veq, mul_def]

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -281,18 +281,13 @@ theorem [anonymous] (a : Fin n) : a.val = a :=
 /-- Assume `k = l`. If two functions defined on `fin k` and `fin l` are equal on each element,
 then they coincide (in the heq sense). -/
 protected theorem heq_fun_iff {α : Sort _} {k l : ℕ} (h : k = l) {f : Fin k → α} {g : Fin l → α} :
-    HEq f g ↔ ∀ i : Fin k, f i = g ⟨(i : ℕ), h ▸ i.2⟩ :=
-  by
-  subst h
-  simp [Function.funext_iff]
+    HEq f g ↔ ∀ i : Fin k, f i = g ⟨(i : ℕ), h ▸ i.2⟩ := by subst h; simp [Function.funext_iff]
 #align fin.heq_fun_iff Fin.heq_fun_iff
 -/
 
 #print Fin.heq_ext_iff /-
 protected theorem heq_ext_iff {k l : ℕ} (h : k = l) {i : Fin k} {j : Fin l} :
-    HEq i j ↔ (i : ℕ) = (j : ℕ) := by
-  subst h
-  simp [coe_eq_coe]
+    HEq i j ↔ (i : ℕ) = (j : ℕ) := by subst h; simp [coe_eq_coe]
 #align fin.heq_ext_iff Fin.heq_ext_iff
 -/
 
@@ -573,10 +568,8 @@ Case conversion may be inaccurate. Consider using '#align fin.eq_zero_or_eq_succ
 theorem eq_zero_or_eq_succ {n : ℕ} (i : Fin (n + 1)) : i = 0 ∨ ∃ j : Fin n, i = j.succ :=
   by
   rcases i with ⟨_ | j, h⟩
-  · left
-    rfl
-  · right
-    exact ⟨⟨j, Nat.lt_of_succ_lt_succ h⟩, rfl⟩
+  · left; rfl
+  · right; exact ⟨⟨j, Nat.lt_of_succ_lt_succ h⟩, rfl⟩
 #align fin.eq_zero_or_eq_succ Fin.eq_zero_or_eq_succ
 
 /- warning: fin.eq_succ_of_ne_zero -> Fin.eq_succ_of_ne_zero is a dubious translation:
@@ -989,10 +982,7 @@ theorem val_add_eq_ite {n : ℕ} (a b : Fin n) :
 #align fin.coe_add_eq_ite Fin.val_add_eq_ite
 
 #print Fin.val_bit0 /-
-theorem val_bit0 {n : ℕ} (k : Fin n) : ((bit0 k : Fin n) : ℕ) = bit0 (k : ℕ) % n :=
-  by
-  cases k
-  rfl
+theorem val_bit0 {n : ℕ} (k : Fin n) : ((bit0 k : Fin n) : ℕ) = bit0 (k : ℕ) % n := by cases k; rfl
 #align fin.coe_bit0 Fin.val_bit0
 -/
 
@@ -1023,9 +1013,7 @@ Case conversion may be inaccurate. Consider using '#align fin.last_add_one Fin.l
 @[simp]
 theorem last_add_one : ∀ n, last n + 1 = 0
   | 0 => Subsingleton.elim _ _
-  | n + 1 => by
-    ext
-    rw [coe_add, coe_zero, coe_last, coe_one, Nat.mod_self]
+  | n + 1 => by ext; rw [coe_add, coe_zero, coe_last, coe_one, Nat.mod_self]
 #align fin.last_add_one Fin.last_add_one
 
 /- warning: fin.coe_add_one -> Fin.val_add_one is a dubious translation:
@@ -1161,10 +1149,8 @@ lean 3 declaration is
 but is expected to have type
   forall (n : Nat), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n) (Fin.last n)
 Case conversion may be inaccurate. Consider using '#align fin.coe_nat_eq_last Fin.cast_nat_eq_lastₓ'. -/
-theorem cast_nat_eq_last (n) : (n : Fin (n + 1)) = Fin.last n :=
-  by
-  rw [← Fin.ofNat_eq_val, Fin.ofNat, Fin.last]
-  simp only [Nat.mod_eq_of_lt n.lt_succ_self]
+theorem cast_nat_eq_last (n) : (n : Fin (n + 1)) = Fin.last n := by
+  rw [← Fin.ofNat_eq_val, Fin.ofNat, Fin.last]; simp only [Nat.mod_eq_of_lt n.lt_succ_self]
 #align fin.coe_nat_eq_last Fin.cast_nat_eq_last
 
 /- warning: fin.le_coe_last -> Fin.le_val_last is a dubious translation:
@@ -1173,10 +1159,7 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n)
 Case conversion may be inaccurate. Consider using '#align fin.le_coe_last Fin.le_val_lastₓ'. -/
-theorem le_val_last (i : Fin (n + 1)) : i ≤ n :=
-  by
-  rw [Fin.cast_nat_eq_last]
-  exact Fin.le_last i
+theorem le_val_last (i : Fin (n + 1)) : i ≤ n := by rw [Fin.cast_nat_eq_last]; exact Fin.le_last i
 #align fin.le_coe_last Fin.le_val_last
 
 end OfNatCoe
@@ -1230,8 +1213,7 @@ theorem zero_eq_one_iff [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 :=
     have := congr_arg (coe : Fin n → ℕ) h
     simp only [Fin.val_zero, ← Nat.dvd_iff_mod_eq_zero, Fin.val_one', @eq_comm _ 0] at this
     exact eq_one_of_dvd_one this
-  · rintro rfl
-    rfl
+  · rintro rfl; rfl
 #align fin.zero_eq_one_iff Fin.zero_eq_one_iff
 
 /- warning: fin.one_eq_zero_iff -> Fin.one_eq_zero_iff is a dubious translation:
@@ -1385,10 +1367,8 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Nat} (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Nat.succ i) (add_lt_add_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i n h (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align fin.mk_succ_pos Fin.mk_succ_posₓ'. -/
-theorem mk_succ_pos (i : ℕ) (h : i < n) : (0 : Fin (n + 1)) < ⟨i.succ, add_lt_add_right h 1⟩ :=
-  by
-  rw [lt_iff_coe_lt_coe, coe_zero]
-  exact Nat.succ_pos i
+theorem mk_succ_pos (i : ℕ) (h : i < n) : (0 : Fin (n + 1)) < ⟨i.succ, add_lt_add_right h 1⟩ := by
+  rw [lt_iff_coe_lt_coe, coe_zero]; exact Nat.succ_pos i
 #align fin.mk_succ_pos Fin.mk_succ_pos
 
 #print Fin.one_lt_succ_succ /-
@@ -1396,8 +1376,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ :=
   by
   cases n
   · exact finZeroElim a
-  · rw [← succ_zero_eq_one, succ_lt_succ_iff]
-    exact succ_pos a
+  · rw [← succ_zero_eq_one, succ_lt_succ_iff]; exact succ_pos a
 #align fin.one_lt_succ_succ Fin.one_lt_succ_succ
 -/
 
@@ -1650,10 +1629,7 @@ theorem cast_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
 
 #print Fin.cast_refl /-
 @[simp]
-theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) :=
-  by
-  ext
-  rfl
+theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) := by ext; rfl
 #align fin.cast_refl Fin.cast_refl
 -/
 
@@ -1671,10 +1647,7 @@ theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
 #print Fin.cast_to_equiv /-
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
-theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
-  by
-  subst h
-  simp
+theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) := by subst h; simp
 #align fin.cast_to_equiv Fin.cast_to_equiv
 -/
 
@@ -1686,10 +1659,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
-theorem cast_eq_cast (h : n = m) : (cast h : Fin n → Fin m) = cast (h ▸ rfl) :=
-  by
-  subst h
-  ext
+theorem cast_eq_cast (h : n = m) : (cast h : Fin n → Fin m) = cast (h ▸ rfl) := by subst h; ext;
   simp
 #align fin.cast_eq_cast Fin.cast_eq_cast
 
@@ -1858,9 +1828,7 @@ theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_succ Fin.cast_castSuccₓ'. -/
 @[simp]
 theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
-    cast h (castSucc i) = castSucc (cast (Nat.succ_injective h) i) :=
-  by
-  ext
+    cast h (castSucc i) = castSucc (cast (Nat.succ_injective h) i) := by ext;
   simp only [coe_cast, coe_cast_succ]
 #align fin.cast_cast_succ Fin.cast_castSucc
 
@@ -2064,10 +2032,8 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Nat} {a : Fin n}, LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (Fin.succ n a)
 Case conversion may be inaccurate. Consider using '#align fin.lt_succ Fin.lt_succₓ'. -/
-theorem lt_succ : a.cast_succ < a.succ :=
-  by
-  rw [cast_succ, lt_iff_coe_lt_coe, coe_cast_add, coe_succ]
-  exact lt_add_one a.val
+theorem lt_succ : a.cast_succ < a.succ := by
+  rw [cast_succ, lt_iff_coe_lt_coe, coe_cast_add, coe_succ]; exact lt_add_one a.val
 #align fin.lt_succ Fin.lt_succ
 
 /- warning: fin.range_cast_succ -> Fin.range_castSucc is a dubious translation:
@@ -2125,10 +2091,7 @@ but is expected to have type
   forall {n : Nat} {i : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_one Fin.addNat_oneₓ'. -/
 @[simp]
-theorem addNat_one {i : Fin n} : addNat 1 i = i.succ :=
-  by
-  ext
-  rw [coe_add_nat, coe_succ]
+theorem addNat_one {i : Fin n} : addNat 1 i = i.succ := by ext; rw [coe_add_nat, coe_succ]
 #align fin.add_nat_one Fin.addNat_one
 
 /- warning: fin.le_coe_add_nat -> Fin.le_coe_addNat is a dubious translation:
@@ -2233,9 +2196,7 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Nat}, Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (Fin.cast n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n))))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_zero Fin.natAdd_zeroₓ'. -/
-theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRelEmbedding :=
-  by
-  ext
+theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRelEmbedding := by ext;
   apply zero_add
 #align fin.nat_add_zero Fin.natAdd_zero
 
@@ -2345,10 +2306,7 @@ but is expected to have type
   forall {n : Nat} (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) j (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))), Eq.{1} Nat (Fin.val n (Fin.pred n j h)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) j) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))
 Case conversion may be inaccurate. Consider using '#align fin.coe_pred Fin.coe_predₓ'. -/
 @[simp]
-theorem coe_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : ℕ) = j - 1 :=
-  by
-  cases j
-  rfl
+theorem coe_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : ℕ) = j - 1 := by cases j; rfl
 #align fin.coe_pred Fin.coe_pred
 
 #print Fin.succ_pred /-
@@ -2366,10 +2324,7 @@ but is expected to have type
   forall {n : Nat} (i : Fin n) {h : Ne.{1} (Fin (Nat.succ n)) (Fin.succ n i) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))}, Eq.{1} (Fin n) (Fin.pred n (Fin.succ n i) h) i
 Case conversion may be inaccurate. Consider using '#align fin.pred_succ Fin.pred_succₓ'. -/
 @[simp]
-theorem pred_succ (i : Fin n) {h : i.succ ≠ 0} : i.succ.pred h = i :=
-  by
-  cases i
-  rfl
+theorem pred_succ (i : Fin n) {h : i.succ ≠ 0} : i.succ.pred h = i := by cases i; rfl
 #align fin.pred_succ Fin.pred_succ
 
 /- warning: fin.pred_eq_iff_eq_succ -> Fin.pred_eq_iff_eq_succ is a dubious translation:
@@ -2455,9 +2410,7 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : ℕ) < n + 1) :
 #print Fin.subNat /-
 /-- `sub_nat i h` subtracts `m` from `i`, generalizes `fin.pred`. -/
 def subNat (m) (i : Fin (n + m)) (h : m ≤ (i : ℕ)) : Fin n :=
-  ⟨(i : ℕ) - m, by
-    rw [tsub_lt_iff_right h]
-    exact i.is_lt⟩
+  ⟨(i : ℕ) - m, by rw [tsub_lt_iff_right h]; exact i.is_lt⟩
 #align fin.sub_nat Fin.subNat
 -/
 
@@ -2793,9 +2746,7 @@ lean 3 declaration is
 but is expected to have type
   forall {a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))} {b : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))}, (Iff (Eq.{1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) a (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Eq.{1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) b (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) -> (Eq.{1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) a b)
 Case conversion may be inaccurate. Consider using '#align fin.fin_two_eq_of_eq_zero_iff Fin.fin_two_eq_of_eq_zero_iffₓ'. -/
-theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b :=
-  by
-  revert a b
+theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b := by revert a b;
   simp [forall_fin_two]
 #align fin.fin_two_eq_of_eq_zero_iff Fin.fin_two_eq_of_eq_zero_iff
 
@@ -2926,8 +2877,7 @@ theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i,
   by
   have : ¬(nat_add m i : ℕ) < m := (le_coe_nat_add _ _).not_lt
   rw [add_cases, dif_neg this]
-  refine' eq_of_hEq ((eq_rec_hEq _ _).trans _)
-  congr 1
+  refine' eq_of_hEq ((eq_rec_hEq _ _).trans _); congr 1
   simp
 #align fin.add_cases_right Fin.addCases_right
 
@@ -3018,10 +2968,8 @@ instance (n : ℕ) [NeZero n] : AddCommGroup (Fin n) :=
       n with
     add_left_neg := fun ⟨a, ha⟩ =>
       Fin.ext <|
-        trans (Nat.mod_add_mod _ _ _) <|
-          by
-          rw [Fin.val_mk, Fin.val_zero, tsub_add_cancel_of_le, Nat.mod_self]
-          exact le_of_lt ha
+        trans (Nat.mod_add_mod _ _ _) <| by
+          rw [Fin.val_mk, Fin.val_zero, tsub_add_cancel_of_le, Nat.mod_self]; exact le_of_lt ha
     sub_eq_add_neg := fun ⟨a, ha⟩ ⟨b, hb⟩ =>
       Fin.ext <| show (a + (n - b)) % n = (a + (n - b) % n) % n by simp
     sub := Fin.sub }
@@ -3189,9 +3137,7 @@ Case conversion may be inaccurate. Consider using '#align fin.succ_above_below F
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
 theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
-    p.succAbove i = i.cast_succ := by
-  rw [succ_above]
-  exact if_pos h
+    p.succAbove i = i.cast_succ := by rw [succ_above]; exact if_pos h
 #align fin.succ_above_below Fin.succAbove_below
 
 /- warning: fin.succ_above_ne_zero_zero -> Fin.succAbove_ne_zero_zero is a dubious translation:
@@ -3250,9 +3196,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_last Fin.succAbove_lastₓ'. -/
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around `last n` embeds by `cast_succ`. -/
 @[simp]
-theorem succAbove_last : succAbove (Fin.last n) = castSucc :=
-  by
-  ext
+theorem succAbove_last : succAbove (Fin.last n) = castSucc := by ext;
   simp only [succ_above_below, cast_succ_lt_last]
 #align fin.succ_above_last Fin.succAbove_last
 
@@ -3367,10 +3311,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_cast_lt Fin.succAbove_castLTₓ'. -/
 @[simp]
 theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
-    (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLT hx) = x :=
-  by
-  rw [succ_above_below, cast_succ_cast_lt]
-  exact h
+    (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLT hx) = x := by
+  rw [succ_above_below, cast_succ_cast_lt]; exact h
 #align fin.succ_above_cast_lt Fin.succAbove_castLT
 
 /- warning: fin.succ_above_pred -> Fin.succAbove_pred is a dubious translation:
@@ -3378,9 +3320,7 @@ theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred Fin.succAbove_predₓ'. -/
 @[simp]
 theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
-    x.succAbove (y.pred hy) = y :=
-  by
-  rw [succ_above_above, succ_pred]
+    x.succAbove (y.pred hy) = y := by rw [succ_above_above, succ_pred];
   simpa [le_iff_coe_le_coe] using Nat.le_pred_of_lt h
 #align fin.succ_above_pred Fin.succAbove_pred
 
@@ -3605,8 +3545,7 @@ theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H
       _ ≤ _ := Nat.pred_le _
       _ ≤ _ := H
       
-  · simp at ha
-    exact le_pred_of_lt (lt_of_le_of_lt ha hb)
+  · simp at ha; exact le_pred_of_lt (lt_of_le_of_lt ha hb)
   · exact H
 #align fin.pred_above_right_monotone Fin.predAbove_right_monotone
 
@@ -3647,11 +3586,7 @@ theorem castPred_zero : castPred (0 : Fin (n + 2)) = 0 :=
 
 #print Fin.castPred_one /-
 @[simp]
-theorem castPred_one : castPred (1 : Fin (n + 2)) = 1 :=
-  by
-  cases n
-  apply Subsingleton.elim
-  rfl
+theorem castPred_one : castPred (1 : Fin (n + 2)) = 1 := by cases n; apply Subsingleton.elim; rfl
 #align fin.cast_pred_one Fin.castPred_one
 -/
 
@@ -3752,14 +3687,8 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
   rcases p with ⟨p, _⟩
   rcases i with ⟨i, _⟩
   cases' lt_or_le i p with H H
-  · rw [dif_neg]
-    rw [if_pos]
-    rfl
-    exact H
-    simp
-    apply le_of_lt H
-  · rw [dif_pos]
-    rw [if_neg]
+  · rw [dif_neg]; rw [if_pos]; rfl; exact H; simp; apply le_of_lt H
+  · rw [dif_pos]; rw [if_neg]
     pick_goal 3
     -- For some reason `simp` doesn't fire fully unless we discharge the third goal.
     · exact lt_of_le_of_ne H (Ne.symm h)
@@ -3796,10 +3725,8 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
 <too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSuccₓ'. -/
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
-    (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' :=
-  by
-  cases a
-  rfl
+    (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' := by
+  cases a; rfl
 #align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSucc
 
 /- warning: fin.pred_succ_above_pred -> Fin.pred_succAbove_pred is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -1532,10 +1532,7 @@ theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i
 #align fin.range_cast_le Fin.range_castLE
 
 /- warning: fin.coe_of_injective_cast_le_symm -> Fin.coe_of_injective_castLE_symm is a dubious translation:
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(x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) 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x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) i hi))) (Fin.val k i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
@@ -1546,10 +1543,7 @@ theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi)
 #align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symm
 
 /- warning: fin.cast_le_succ -> Fin.castLE_succ is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_succ Fin.castLE_succₓ'. -/
 @[simp]
 theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
@@ -1624,10 +1618,7 @@ theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
 #align fin.cast_zero Fin.cast_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_last Fin.cast_lastₓ'. -/
 @[simp]
 theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
@@ -1775,10 +1766,7 @@ theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt
 #align fin.cast_lt_cast_add Fin.castLT_castAdd
 
 /- warning: fin.cast_add_cast -> Fin.castAdd_cast is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -1787,10 +1775,7 @@ theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
 #align fin.cast_add_cast Fin.castAdd_cast
 
 /- warning: fin.cast_cast_add_left -> Fin.cast_castAdd_left is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_add_left Fin.cast_castAdd_leftₓ'. -/
 theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (castAdd m i) = castAdd m (cast (add_right_cancel h) i) :=
@@ -1798,10 +1783,7 @@ theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 #align fin.cast_cast_add_left Fin.cast_castAdd_left
 
 /- warning: fin.cast_cast_add_right -> Fin.cast_castAdd_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_add_right Fin.cast_castAdd_rightₓ'. -/
 @[simp]
 theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
@@ -1810,10 +1792,7 @@ theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
 #align fin.cast_cast_add_right Fin.cast_castAdd_right
 
 /- warning: fin.cast_add_cast_add -> Fin.castAdd_castAdd is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast_add Fin.castAdd_castAddₓ'. -/
 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
     castAdd p (castAdd n i) = cast (add_assoc _ _ _).symm (castAdd (n + p) i) :=
@@ -1875,10 +1854,7 @@ theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt
 #align fin.cast_succ_mk Fin.castSucc_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_succ Fin.cast_castSuccₓ'. -/
 @[simp]
 theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
@@ -2009,10 +1985,7 @@ theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
 #align fin.cast_succ_zero Fin.castSucc_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_one Fin.castSucc_oneₓ'. -/
 @[simp]
 theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
@@ -2052,10 +2025,7 @@ theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a 
 #align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iff
 
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 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_fin_succ Fin.castSucc_fin_succₓ'. -/
 theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.succ (castSucc j) := by
   simp [Fin.ext_iff]
@@ -2112,10 +2082,7 @@ theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) =
 #align fin.range_cast_succ Fin.range_castSucc
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
@@ -2126,10 +2093,7 @@ theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
 #align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symm
 
 /- warning: fin.succ_cast_succ -> Fin.succ_castSucc is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_cast_succ Fin.succ_castSuccₓ'. -/
 theorem succ_castSucc {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
   Fin.ext (by simp)
@@ -2189,10 +2153,7 @@ theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, ad
 #align fin.add_nat_mk Fin.addNat_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_zero Fin.cast_addNat_zeroₓ'. -/
 @[simp]
 theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
@@ -2201,10 +2162,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 #align fin.cast_add_nat_zero Fin.cast_addNat_zero
 
 /- warning: fin.add_nat_cast -> Fin.addNat_cast is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2213,10 +2171,7 @@ theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
 #align fin.add_nat_cast Fin.addNat_cast
 
 /- warning: fin.cast_add_nat_left -> Fin.cast_addNat_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_left Fin.cast_addNat_leftₓ'. -/
 theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (addNat m i) = addNat m (cast (add_right_cancel h) i) :=
@@ -2224,10 +2179,7 @@ theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 #align fin.cast_add_nat_left Fin.cast_addNat_left
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_right Fin.cast_addNat_rightₓ'. -/
 @[simp]
 theorem cast_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
@@ -2288,10 +2240,7 @@ theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRe
 #align fin.nat_add_zero Fin.natAdd_zero
 
 /- warning: fin.nat_add_cast -> Fin.natAdd_cast is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast Fin.natAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
 theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2300,10 +2249,7 @@ theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
 #align fin.nat_add_cast Fin.natAdd_cast
 
 /- warning: fin.cast_nat_add_right -> Fin.cast_natAdd_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_right Fin.cast_natAdd_rightₓ'. -/
 theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
     cast h (natAdd m i) = natAdd m (cast (add_left_cancel h) i) :=
@@ -2311,10 +2257,7 @@ theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
 #align fin.cast_nat_add_right Fin.cast_natAdd_right
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_left Fin.cast_natAdd_leftₓ'. -/
 @[simp]
 theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
@@ -2323,10 +2266,7 @@ theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
 #align fin.cast_nat_add_left Fin.cast_natAdd_left
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_add Fin.castAdd_natAddₓ'. -/
 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     castAdd p (natAdd m i) = cast (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
@@ -2334,10 +2274,7 @@ theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
 #align fin.cast_add_nat_add Fin.castAdd_natAdd
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast_add Fin.natAdd_castAddₓ'. -/
 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     natAdd m (castAdd p i) = cast (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
@@ -2345,10 +2282,7 @@ theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
 #align fin.nat_add_cast_add Fin.natAdd_castAdd
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_nat_add Fin.natAdd_natAddₓ'. -/
 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
     natAdd m (natAdd n i) = cast (add_assoc _ _ _) (natAdd (m + n) i) :=
@@ -2356,10 +2290,7 @@ theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
 #align fin.nat_add_nat_add Fin.natAdd_natAdd
 
 /- warning: fin.cast_nat_add_zero -> Fin.cast_natAdd_zero is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_zero Fin.cast_natAdd_zeroₓ'. -/
 @[simp]
 theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
@@ -2368,10 +2299,7 @@ theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
 #align fin.cast_nat_add_zero Fin.cast_natAdd_zero
 
 /- warning: fin.cast_nat_add -> Fin.cast_natAdd is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add Fin.cast_natAddₓ'. -/
 @[simp]
 theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAdd n i) = addNat n i :=
@@ -2379,10 +2307,7 @@ theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAd
 #align fin.cast_nat_add Fin.cast_natAdd
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat Fin.cast_addNatₓ'. -/
 @[simp]
 theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNat m i) = natAdd m i :=
@@ -2390,10 +2315,7 @@ theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNa
 #align fin.cast_add_nat Fin.cast_addNat
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_last Fin.natAdd_lastₓ'. -/
 @[simp]
 theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
@@ -2401,10 +2323,7 @@ theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
 #align fin.nat_add_last Fin.natAdd_last
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast_succ Fin.natAdd_castSuccₓ'. -/
 theorem natAdd_castSucc {m n : ℕ} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
   rfl
@@ -2562,10 +2481,7 @@ theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
 #align fin.sub_nat_mk Fin.subNat_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.pred_cast_succ_succ Fin.pred_castSucc_succₓ'. -/
 @[simp]
 theorem pred_castSucc_succ (i : Fin n) :
@@ -2597,10 +2513,7 @@ theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addN
 #align fin.sub_nat_add_nat Fin.subNat_addNat
 
 /- warning: fin.nat_add_sub_nat_cast -> Fin.natAdd_subNat_cast is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castₓ'. -/
 @[simp]
 theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
@@ -2740,10 +2653,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 #align fin.induction_zero Fin.induction_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2929,10 +2839,7 @@ theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (F
 #align fin.reverse_induction_last Fin.reverse_induction_last
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSuccₓ'. -/
 @[simp]
 theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
@@ -2972,10 +2879,7 @@ theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.la
 #align fin.last_cases_last Fin.lastCases_last
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.last_cases_cast_succ Fin.lastCases_castSuccₓ'. -/
 @[simp]
 theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
@@ -3000,10 +2904,7 @@ def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd
 #align fin.add_cases Fin.addCases
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.add_cases_left Fin.addCases_leftₓ'. -/
 @[simp]
 theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
@@ -3016,10 +2917,7 @@ theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C
 #align fin.add_cases_left Fin.addCases_left
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.add_cases_right Fin.addCases_rightₓ'. -/
 @[simp]
 theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
@@ -3265,10 +3163,7 @@ end AddGroup
 section SuccAbove
 
 /- warning: fin.succ_above_aux -> Fin.succAbove_aux is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_aux Fin.succAbove_auxₓ'. -/
 theorem succAbove_aux (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
@@ -3289,10 +3184,7 @@ def succAbove (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
 #align fin.succ_above Fin.succAbove
 
 /- warning: fin.succ_above_below -> Fin.succAbove_below is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_below Fin.succAbove_belowₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
@@ -3365,20 +3257,14 @@ theorem succAbove_last : succAbove (Fin.last n) = castSucc :=
 #align fin.succ_above_last Fin.succAbove_last
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_last_apply Fin.succAbove_last_applyₓ'. -/
 theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_succ := by
   rw [succ_above_last]
 #align fin.succ_above_last_apply Fin.succAbove_last_apply
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_above Fin.succAbove_aboveₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
@@ -3387,10 +3273,7 @@ theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
 #align fin.succ_above_above Fin.succAbove_above
 
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 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_ge Fin.succAbove_lt_geₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p ≤ i.cast_succ :=
@@ -3410,10 +3293,7 @@ theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p <
 #align fin.succ_above_lt_gt Fin.succAbove_lt_gt
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_iff Fin.succAbove_lt_iffₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
@@ -3432,10 +3312,7 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
 #align fin.succ_above_lt_iff Fin.succAbove_lt_iff
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.lt_succ_above_iff Fin.lt_succAbove_iffₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
@@ -3497,10 +3374,7 @@ theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
 #align fin.succ_above_cast_lt Fin.succAbove_castLT
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred Fin.succAbove_predₓ'. -/
 @[simp]
 theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
@@ -3511,10 +3385,7 @@ theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_
 #align fin.succ_above_pred Fin.succAbove_pred
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_succ_above Fin.castLT_succAboveₓ'. -/
 theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
     (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
@@ -3522,10 +3393,7 @@ theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
 #align fin.cast_lt_succ_above Fin.castLT_succAbove
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above Fin.pred_succAboveₓ'. -/
 theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
     (h' : y.succAbove x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
@@ -3604,10 +3472,7 @@ theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
 #align fin.succ_above_right_injective Fin.succAbove_right_injective
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_right_inj Fin.succAbove_right_injₓ'. -/
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b ↔ a = b :=
@@ -3660,10 +3525,7 @@ theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove
 #align fin.succ_succ_above_zero Fin.succ_succAbove_zero
 
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 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_succ Fin.succ_succAbove_succₓ'. -/
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
@@ -3680,10 +3542,7 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
 #align fin.succ_succ_above_succ Fin.succ_succAbove_succ
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_zero Fin.one_succAbove_zeroₓ'. -/
 @[simp]
 theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
@@ -3691,10 +3550,7 @@ theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
 #align fin.one_succ_above_zero Fin.one_succAbove_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_one Fin.succ_succAbove_oneₓ'. -/
 /-- By moving `succ` to the outside of this expression, we create opportunities for further
 simplification using `succ_above_zero` or `succ_succ_above_zero`. -/
@@ -3705,10 +3561,7 @@ theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
 #align fin.succ_succ_above_one Fin.succ_succAbove_one
 
 /- warning: fin.one_succ_above_succ -> Fin.one_succAbove_succ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_succ Fin.one_succAbove_succₓ'. -/
 @[simp]
 theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j.succ = j.succ.succ :=
@@ -3716,10 +3569,7 @@ theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j
 #align fin.one_succ_above_succ Fin.one_succAbove_succ
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_one Fin.one_succAbove_oneₓ'. -/
 @[simp]
 theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 :=
@@ -3846,10 +3696,7 @@ theorem coe_castPred {n : ℕ} (a : Fin (n + 2)) (hx : a < Fin.last _) : (a.cast
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_below Fin.predAbove_belowₓ'. -/
 theorem predAbove_below (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_succ) :
     p.predAbove i = i.cast_pred :=
@@ -3876,10 +3723,7 @@ theorem predAbove_last_apply (i : Fin n) : predAbove (Fin.last n) i = i.cast_pre
 #align fin.pred_above_last_apply Fin.predAbove_last_apply
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_above Fin.predAbove_aboveₓ'. -/
 theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
     p.predAbove i = i.pred (p.cast_succ.zero_le.trans_lt h).Ne.symm := by simp [pred_above, h]
@@ -3896,10 +3740,7 @@ theorem castPred_monotone : Monotone (@castPred n) :=
 #align fin.cast_pred_monotone Fin.castPred_monotone
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred_above Fin.succAbove_predAboveₓ'. -/
 /-- Sending `fin (n+1)` to `fin n` by subtracting one from anything above `p`
 then back to `fin (n+1)` with a gap around `p` is the identity away from `p`. -/
@@ -3929,10 +3770,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
 
 /- warning: fin.pred_above_succ_above -> Fin.predAbove_succAbove is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_succ_above Fin.predAbove_succAboveₓ'. -/
 /-- Sending `fin n` into `fin (n + 1)` with a gap at `p`
 then back to `fin n` by subtracting one from anything above `p` is the identity. -/
@@ -3955,10 +3793,7 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
 #align fin.pred_above_succ_above Fin.predAbove_succAbove
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSuccₓ'. -/
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
     (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' :=
@@ -3968,10 +3803,7 @@ theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
 #align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSucc
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above_pred Fin.pred_succAbove_predₓ'. -/
 /-- `pred` commutes with `succ_above`. -/
 theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
@@ -4019,10 +3851,7 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_pred_cast_succ Fin.castPred_castSuccₓ'. -/
 @[simp]
 theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
@@ -4030,10 +3859,7 @@ theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
 #align fin.cast_pred_cast_succ Fin.castPred_castSucc
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_pred Fin.castSucc_castPredₓ'. -/
 theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSucc i.cast_pred = i :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -603,7 +603,7 @@ def rev : Equiv.Perm (Fin n) :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.Perm.{1} (Fin n)) (fun (_x : Equiv.{1, 1} (Fin n) (Fin n)) => (Fin n) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align fin.coe_rev Fin.val_revₓ'. -/
 @[simp]
 theorem val_rev (i : Fin n) : (i.rev : ℕ) = n - (i + 1) :=
@@ -695,7 +695,7 @@ def revOrderIso {n} : (Fin n)ᵒᵈ ≃o Fin n :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (OrderDual.{0} (Fin n)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (Fin.hasLe n) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n))) (fun (_x : RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)))) => (Fin n) -> (OrderDual.{0} (Fin n))) (RelIso.hasCoeToFun.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)))) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)) (Fin.hasLe n) (Fin.revOrderIso n)) i) (coeFn.{1, 1} (Equiv.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (fun (_x : Equiv.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) => (Fin n) -> (OrderDual.{0} (Fin n))) (Equiv.hasCoeToFun.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (OrderDual.toDual.{0} (Fin n)) (coeFn.{1, 1} (Equiv.Perm.{1} (Fin n)) (fun (_x : Equiv.{1, 1} (Fin n) (Fin n)) => (Fin n) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} (OrderDual.{0} (Fin n)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => OrderDual.{0} (Fin n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) (instLEFin n) (Fin.revOrderIso n)) i) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (fun (_x : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) _x) (Equiv.instFunLikeEquiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) (OrderDual.toDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
+  forall {n : Nat} (i : Fin n), Eq.{1} (OrderDual.{0} (Fin n)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => OrderDual.{0} (Fin n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) (instLEFin n) (Fin.revOrderIso n)) i) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i))) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i) (fun (_x : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i) => OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i)) _x) (Equiv.instFunLikeEquiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i))) (OrderDual.toDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) i)) (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
 Case conversion may be inaccurate. Consider using '#align fin.rev_order_iso_symm_apply Fin.revOrderIso_symm_applyₓ'. -/
 @[simp]
 theorem revOrderIso_symm_apply (i : Fin n) : revOrderIso.symm i = OrderDual.toDual i.rev :=
@@ -784,7 +784,7 @@ open Set
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (e : OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) e i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} (e : OrderIso.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e i)) (Fin.val n i)
+  forall {n : Nat} {m : Nat} (e : OrderIso.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_order_iso_apply Fin.coe_orderIso_applyₓ'. -/
 /-- If `e` is an `order_iso` between `fin n` and `fin m`, then `n = m` and `e` is the identity
 map. In this lemma we state that for each `i : fin n` we have `(e i : ℕ) = (i : ℕ)`. -/
@@ -849,7 +849,7 @@ theorem strictMono_unique {f g : Fin n → α} (hf : StrictMono f) (hg : StrictM
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) f)) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)) f g)
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f)) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) f g)
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) f)) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) f g)
 Case conversion may be inaccurate. Consider using '#align fin.order_embedding_eq Fin.orderEmbedding_eqₓ'. -/
 /-- Two order embeddings of `fin n` are equal provided that their ranges are equal. -/
 theorem orderEmbedding_eq {f g : Fin n ↪o α} (h : range f = range g) : f = g :=
@@ -1284,7 +1284,7 @@ def succEmbedding (n : ℕ) : Fin n ↪o Fin (n + 1) :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succEmbedding n)) (Fin.succ n)
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succEmbedding n)) (Fin.succ n)
+  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succEmbedding n)) (Fin.succ n)
 Case conversion may be inaccurate. Consider using '#align fin.coe_succ_embedding Fin.val_succEmbeddingₓ'. -/
 @[simp]
 theorem val_succEmbedding : ⇑(succEmbedding n) = Fin.succ :=
@@ -1491,7 +1491,7 @@ def castLE (h : n ≤ m) : Fin n ↪o Fin m :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe n m) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE n m h) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n m h) i)) (Fin.val n i)
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n m h) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast_le Fin.coe_castLEₓ'. -/
 @[simp]
 theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
@@ -1502,7 +1502,7 @@ theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
 lean 3 declaration is
   forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat Nat.hasLt i n) (h : LE.le.{0} Nat Nat.hasLe n m), Eq.{1} (Fin m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) i n m hn h))
 but is expected to have type
-  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat instLTNat i n) (h : LE.le.{0} Nat instLENat n m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin m) (Fin.mk n i hn)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn h))
+  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat instLTNat i n) (h : LE.le.{0} Nat instLENat n m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin m) (Fin.mk n i hn)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_mk Fin.castLE_mkₓ'. -/
 @[simp]
 theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
@@ -1514,7 +1514,7 @@ theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe (Nat.succ n) (Nat.succ m)), Eq.{1} (Fin (Nat.succ m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ m))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) (Fin.castLE (Nat.succ n) (Nat.succ m) h) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (OfNat.mk.{0} (Fin (Nat.succ n)) 0 (Zero.zero.{0} (Fin (Nat.succ n)) (Fin.hasZeroOfNeZero (Nat.succ n) (NeZero.succ n)))))) (OfNat.ofNat.{0} (Fin (Nat.succ m)) 0 (OfNat.mk.{0} (Fin (Nat.succ m)) 0 (Zero.zero.{0} (Fin (Nat.succ m)) (Fin.hasZeroOfNeZero (Nat.succ m) (NeZero.succ m)))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat (Nat.succ n) (Nat.succ m)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (instLEFin (Nat.succ n)) (instLEFin (Nat.succ m))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (Nat.succ m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (instLEFin (Nat.succ n)) (instLEFin (Nat.succ m))) (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE (Nat.succ n) (Nat.succ m) h) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) 0 (Fin.instOfNatFin (Nat.succ m) 0 (NeZero.succ m)))
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat (Nat.succ n) (Nat.succ m)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (instLEFin (Nat.succ n)) (instLEFin (Nat.succ m))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (Nat.succ m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (instLEFin (Nat.succ n)) (instLEFin (Nat.succ m))) (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE (Nat.succ n) (Nat.succ m) h) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) 0 (Fin.instOfNatFin (Nat.succ m) 0 (NeZero.succ m)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_zero Fin.castLE_zeroₓ'. -/
 @[simp]
 theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [eq_iff_veq]
@@ -1524,7 +1524,7 @@ theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by s
 lean 3 declaration is
   forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (Fin.hasLe n) (Fin.hasLe k)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i) n))
 but is expected to have type
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (instLEFin n) (instLEFin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (instLEFin n) (instLEFin k)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n k h))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat instLTNat (Fin.val k i) n))
+  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (instLEFin n) (instLEFin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (instLEFin n) (instLEFin k)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat instLTNat (Fin.val k i) n))
 Case conversion may be inaccurate. Consider using '#align fin.range_cast_le Fin.range_castLEₓ'. -/
 @[simp]
 theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i : ℕ) < n } :=
@@ -1535,7 +1535,7 @@ theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i
 lean 3 declaration is
   forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k) (i : Fin k) (hi : Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) => (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k)) (Fin.castLE n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) i hi))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i)
 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 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(FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) 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x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n k h)))) i hi))) (Fin.val k i)
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k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) (Fin n)) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) a) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) (fun (_x : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) a) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) a) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (Fin.castLE n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE n k h)))) i hi))) (Fin.val k i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
@@ -1549,7 +1549,7 @@ theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi)
 lean 3 declaration is
   forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat Nat.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) (Fin.succ m i)) (Fin.succ n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat Nat.hasLe (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe m n) (Nat.succ_le_succ_iff m n) h)) i))
 but is expected to have type
-  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat instLENat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ m i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) (Fin.succ m i)) (Fin.succ n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat instLENat (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat instLENat m n) (Nat.succ_le_succ_iff m n) h)) i))
+  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat instLENat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ m i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) (Fin.succ m i)) (Fin.succ n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat instLENat (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat instLENat m n) (Nat.succ_le_succ_iff m n) h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_succ Fin.castLE_succₓ'. -/
 @[simp]
 theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
@@ -1560,7 +1560,7 @@ theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
 lean 3 declaration is
   forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n) (i : Fin k), Eq.{1} (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n mn) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE k m km) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)) i)
 but is expected to have type
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n) (i : Fin k), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (a : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin m) a) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k m km) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n mn) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k m km) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn)) i)
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n) (i : Fin k), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (a : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin k) => Fin m) a) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE k m km) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE m n mn) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin k) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE k m km) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin k) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_cast_le Fin.castLE_castLEₓ'. -/
 @[simp]
 theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
@@ -1572,7 +1572,7 @@ theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
 lean 3 declaration is
   forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n mn)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE k m km))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)))
 but is expected to have type
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n mn)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k m km))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn)))
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE m n mn)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin k) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE k m km))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin k) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_comp_cast_le Fin.castLE_comp_castLEₓ'. -/
 @[simp]
 theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
@@ -1600,7 +1600,7 @@ theorem symm_cast (h : n = m) : (cast h).symm = cast h.symm :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h) i)) (Fin.val n i)
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n m h) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast Fin.coe_castₓ'. -/
 /-- While `fin.coe_order_iso_apply` is a more general case of this, we mark this `simp` anyway
 as it is eligible for `dsimp`. -/
@@ -1613,7 +1613,7 @@ theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : ℕ) = i :=
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {h : Eq.{1} Nat n n'}, Eq.{1} (Fin n') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' h) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin n') 0 (OfNat.mk.{0} (Fin n') 0 (Zero.zero.{0} (Fin n') (Fin.hasZeroOfNeZero n' (Eq.mpr.{0} (NeZero.{0} Nat Nat.hasZero n') (NeZero.{0} Nat Nat.hasZero n) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (NeZero.{0} Nat Nat.hasZero n') (NeZero.{0} Nat Nat.hasZero n)) (Eq.ndrec.{0, 1} Nat n' (fun (_a : Nat) => Eq.{1} Prop (NeZero.{0} Nat Nat.hasZero n') (NeZero.{0} Nat Nat.hasZero _a)) (rfl.{1} Prop (NeZero.{0} Nat Nat.hasZero n')) n (Eq.symm.{1} Nat n n' h))) _inst_1)))))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {h : Eq.{1} Nat n n'}, Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' h) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ([mdata noImplicitLambda:1 Fin n']) 0 (Fin.instOfNatFin n' 0 (Eq.mpr.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) (id.{0} (Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n)) (Eq.ndrec.{0, 1} Nat n' (fun (_a : Nat) => Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) _a)) (Eq.refl.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n')) n (Eq.symm.{1} Nat n n' h))) (inferInstance.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) _inst_1))))
+  forall {n : Nat} {n' : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {h : Eq.{1} Nat n n'}, Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n n' h) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ([mdata noImplicitLambda:1 Fin n']) 0 (Fin.instOfNatFin n' 0 (Eq.mpr.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) (id.{0} (Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n)) (Eq.ndrec.{0, 1} Nat n' (fun (_a : Nat) => Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) _a)) (Eq.refl.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n')) n (Eq.symm.{1} Nat n n' h))) (inferInstance.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.cast_zero Fin.cast_zeroₓ'. -/
 @[simp]
 theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
@@ -1627,7 +1627,7 @@ theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) (Fin.last n)) (Fin.last n')
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) (Fin.last n)) (Fin.last n')
+  forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) (Fin.last n)) (Fin.last n')
 Case conversion may be inaccurate. Consider using '#align fin.cast_last Fin.cast_lastₓ'. -/
 @[simp]
 theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
@@ -1638,7 +1638,7 @@ theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Nat) (hn : LT.lt.{0} Nat Nat.hasLt i n), Eq.{1} (Fin m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) i n m hn (Eq.le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) n m h)))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Nat) (hn : LT.lt.{0} Nat instLTNat i n), Eq.{1} (Fin m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn (Eq.le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) n m h)))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Nat) (hn : LT.lt.{0} Nat instLTNat i n), Eq.{1} (Fin m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn (Eq.le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) n m h)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_mk Fin.cast_mkₓ'. -/
 @[simp]
 theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h.le⟩ :=
@@ -1649,7 +1649,7 @@ theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i,
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {k : Nat} (h : Eq.{1} Nat n m) (h' : Eq.{1} Nat m k) {i : Fin n}, Eq.{1} (Fin k) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin m) (Fin k) (Fin.hasLe m) (Fin.hasLe k)) (fun (_x : RelIso.{0, 0} (Fin m) (Fin k) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin m) -> (Fin k)) (RelIso.hasCoeToFun.{0, 0} (Fin m) (Fin k) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.cast m k h') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin k) (Fin.hasLe n) (Fin.hasLe k)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.cast n k (Eq.trans.{1} Nat n m k h h')) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} {k : Nat} (h : Eq.{1} Nat n m) (h' : Eq.{1} Nat m k) {i : Fin n}, Eq.{1} (Fin k) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (fun (_x : Fin m) => Fin k) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast m k h') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin k) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n k (Eq.trans.{1} Nat n m k h h')) i)
+  forall {n : Nat} {m : Nat} {k : Nat} (h : Eq.{1} Nat n m) (h' : Eq.{1} Nat m k) {i : Fin n}, Eq.{1} (Fin k) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin m) (fun (_x : Fin m) => Fin k) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast m k h') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n m h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin k) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n k (Eq.trans.{1} Nat n m k h h')) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_trans Fin.cast_transₓ'. -/
 @[simp]
 theorem cast_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
@@ -1670,7 +1670,7 @@ theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) :=
 lean 3 declaration is
   forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat Nat.hasLe m n}, Eq.{1} ((fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (Fin.castLE m n h')) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n h')) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast m n h))
 but is expected to have type
-  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat instLENat m n}, Eq.{1} (forall (a : Fin m), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n h')) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (fun (_x : Fin m) => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast m n h))
+  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat instLENat m n}, Eq.{1} (forall (a : Fin m), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castLE m n h')) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin m) (fun (_x : Fin m) => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast m n h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_of_eq Fin.castLE_of_eqₓ'. -/
 theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
     (castLE h' : Fin m → Fin n) = Fin.cast h :=
@@ -1691,7 +1691,7 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (Fin.cast n m h)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h)) (cast.{1} (Fin n) (Fin m) (Eq.subst.{1} Nat (fun (_x : Nat) => Eq.{2} Type (Fin n) (Fin _x)) n m h (rfl.{2} Type (Fin n))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((Fin n) -> (Fin m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8777 : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8320 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8321 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8320) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8320) (rfl.{1} Nat n) m h)))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((Fin n) -> (Fin m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n m h)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8798 : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8320 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8321 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8320) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8320) (rfl.{1} Nat n) m h)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
@@ -1713,7 +1713,7 @@ def castAdd (m) : Fin n ↪o Fin (n + m) :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) i)) (Fin.val n i)
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n m) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast_add Fin.coe_castAddₓ'. -/
 @[simp]
 theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
@@ -1724,7 +1724,7 @@ theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} ((fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n) (Fin.hasLe n) (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n) -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n n (rfl.{1} Nat n)))
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n (rfl.{1} Nat n)))
+  forall {n : Nat}, Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n n (rfl.{1} Nat n)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_zero Fin.castAdd_zeroₓ'. -/
 @[simp]
 theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = cast rfl :=
@@ -1735,7 +1735,7 @@ theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = cast rfl :=
 lean 3 declaration is
   forall {m : Nat} (n : Nat) (i : Fin m), LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) m
 but is expected to have type
-  forall {m : Nat} (n : Nat) (i : Fin m), LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) m
+  forall {m : Nat} (n : Nat) (i : Fin m), LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd m n) i)) m
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_lt Fin.castAdd_ltₓ'. -/
 theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAdd n i : ℕ) < m :=
   i.2
@@ -1745,7 +1745,7 @@ theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAdd n i : ℕ) < m :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Nat) (h : LT.lt.{0} Nat Nat.hasLt i n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i (Nat.lt_add_right i n m h))
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i (Nat.lt_add_right i n m h))
+  forall {n : Nat} (m : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n m) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i (Nat.lt_add_right i n m h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_mk Fin.castAdd_mkₓ'. -/
 @[simp]
 theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i, lt_add_right i n m h⟩ :=
@@ -1756,7 +1756,7 @@ theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (hi : LT.lt.{0} Nat Nat.hasLt (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i hi)) i
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (hi : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i) n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) i
+  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (hi : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i) n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n m) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast_lt Fin.castAdd_castLTₓ'. -/
 @[simp]
 theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m (castLT i hi) = i :=
@@ -1767,7 +1767,7 @@ theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i) (Fin.castAdd_lt n m i)) i
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) i) (Fin.castAdd_lt n m i)) i
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n m) i) (Fin.castAdd_lt n m i)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_add Fin.castLT_castAddₓ'. -/
 @[simp]
 theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt m i) = i :=
@@ -1778,7 +1778,7 @@ theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8777 : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n h) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) 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x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (n' : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n' m) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -1790,7 +1790,7 @@ theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n (add_right_cancel.{0} Nat Nat.hasAdd (AddRightCancelSemigroup.toIsRightCancelAdd.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) n' m n h)) i))
 but is expected to have type
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(instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n' m) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n' n (add_right_cancel.{0} Nat instAddNat (IsCancelAdd.toIsRightCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n' m n h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_add_left Fin.cast_castAdd_leftₓ'. -/
 theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (castAdd m i) = castAdd m (cast (add_right_cancel h) i) :=
@@ -1801,7 +1801,7 @@ theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')))) (Fin.castAdd n m') i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun 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(RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n m) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_add_right Fin.cast_castAdd_rightₓ'. -/
 @[simp]
 theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
@@ -1813,7 +1813,7 @@ theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
 lean 3 declaration is
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Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) n p))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m n) p))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) n p))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m n) p)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) n p))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} 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 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast_add Fin.castAdd_castAddₓ'. -/
 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
     castAdd p (castAdd n i) = cast (add_assoc _ _ _).symm (castAdd (n + p) i) :=
@@ -1824,7 +1824,7 @@ theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (Nat.succ n) (Nat.succ n')), Eq.{1} (Fin (Nat.succ n')) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ n'))) (fun (_x : RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ n'))) (RelIso.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) (Fin.cast (Nat.succ n) (Nat.succ n') h) (Fin.succ n i)) (Fin.succ n' (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' (Nat.succ.inj n n' h)) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (Nat.succ n) (Nat.succ n')), Eq.{1} (Fin (Nat.succ n')) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => Fin (Nat.succ n')) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (Nat.succ n) (Nat.succ n') h) (Fin.succ n i)) (Fin.succ n' (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' (Nat.succ.inj n n' h)) i))
+  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (Nat.succ n) (Nat.succ n')), Eq.{1} (Fin (Nat.succ n')) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => Fin (Nat.succ n')) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (Nat.succ n) (Nat.succ n') h) (Fin.succ n i)) (Fin.succ n' (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n n' (Nat.succ.inj n n' h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_eq Fin.cast_succ_eqₓ'. -/
 /-- The cast of the successor is the succesor of the cast. See `fin.succ_cast_eq` for rewriting in
 the reverse direction. -/
@@ -1838,7 +1838,7 @@ theorem cast_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat n n'), Eq.{1} (Fin (Nat.succ n')) (Fin.succ n' (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ n'))) (fun (_x : RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ n'))) (RelIso.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) (Fin.cast (Nat.succ n) (Nat.succ n') (Eq.mpr.{0} (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n')) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n'))) (Eq.ndrec.{0, 1} Nat n (fun (_a : Nat) => Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ _a) (Nat.succ n'))) (rfl.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n'))) n' h)) (rfl.{1} Nat (Nat.succ n')))) (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat n n'), Eq.{1} (Fin (Nat.succ n')) (Fin.succ n' (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => Fin (Nat.succ n')) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (Nat.succ n) (Nat.succ n') (Eq.mpr.{0} (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n')) (id.{0} (Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n'))) (Eq.ndrec.{0, 1} Nat n (fun (_a : Nat) => Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ _a) (Nat.succ n'))) (Eq.refl.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n'))) n' h)) (Eq.refl.{1} Nat (Nat.succ n')))) (Fin.succ n i))
+  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat n n'), Eq.{1} (Fin (Nat.succ n')) (Fin.succ n' (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n n' h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => Fin (Nat.succ n')) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (Nat.succ n) (Nat.succ n') (Eq.mpr.{0} (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n')) (id.{0} (Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n'))) (Eq.ndrec.{0, 1} Nat n (fun (_a : Nat) => Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ _a) (Nat.succ n'))) (Eq.refl.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n'))) n' h)) (Eq.refl.{1} Nat (Nat.succ n')))) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_cast_eq Fin.succ_cast_eqₓ'. -/
 theorem succ_cast_eq {n' : ℕ} (i : Fin n) (h : n = n') :
     (cast h i).succ = cast (by rw [h]) i.succ :=
@@ -1856,7 +1856,7 @@ def castSucc : Fin n ↪o Fin (n + 1) :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (Fin.val n i)
+  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast_succ Fin.coe_castSuccₓ'. -/
 @[simp]
 theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
@@ -1867,7 +1867,7 @@ theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
 lean 3 declaration is
   forall (n : Nat) (i : Nat) (h : LT.lt.{0} Nat Nat.hasLt i n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i (Nat.lt.step i n h))
 but is expected to have type
-  forall (n : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i (Nat.lt.step i n h))
+  forall (n : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i (Nat.lt.step i n h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_mk Fin.castSucc_mkₓ'. -/
 @[simp]
 theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
@@ -1878,7 +1878,7 @@ theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {i : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin 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 but is expected to have type
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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n n' (Nat.succ_injective n n' h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_succ Fin.cast_castSuccₓ'. -/
 @[simp]
 theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
@@ -1892,7 +1892,7 @@ theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) (Fin.succ n i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) (Fin.succ n i)
+  forall {n : Nat} (i : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_succ Fin.castSucc_lt_succₓ'. -/
 theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
   lt_iff_val_lt_val.2 <| by simp only [coe_cast_succ, coe_succ, Nat.lt_succ_self]
@@ -1902,7 +1902,7 @@ theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
 lean 3 declaration is
   forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {j : Fin n}, Iff (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) j)) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i (Fin.succ n j))
 but is expected to have type
-  forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin n}, Iff (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) j)) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (Fin.succ n j))
+  forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin n}, Iff (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) j)) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (Fin.succ n j))
 Case conversion may be inaccurate. Consider using '#align fin.le_cast_succ_iff Fin.le_castSucc_iffₓ'. -/
 theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
   simpa [lt_iff_coe_lt_coe, le_iff_coe_le_coe] using nat.succ_le_succ_iff.symm
@@ -1912,7 +1912,7 @@ theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i
 lean 3 declaration is
   forall {n : Nat} {i : Fin n} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) j) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n)) (Fin.succ n i) j)
 but is expected to have type
-  forall {n : Nat} {i : Fin n} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) j) (LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) (Fin.succ n i) j)
+  forall {n : Nat} {i : Fin n} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i) j) (LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) (Fin.succ n i) j)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_iff_succ_le Fin.castSucc_lt_iff_succ_leₓ'. -/
 theorem castSucc_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
     i.cast_succ < j ↔ i.succ ≤ j := by
@@ -1938,7 +1938,7 @@ theorem succ_eq_last_succ {n : ℕ} (i : Fin n.succ) : i.succ = last (n + 1) ↔
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i h)) i
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) i
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_lt Fin.castSucc_castLTₓ'. -/
 @[simp]
 theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT i h) = i :=
@@ -1949,7 +1949,7 @@ theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT
 lean 3 declaration is
   forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) h) a
 but is expected to have type
-  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat instLTNat (Fin.val n a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) h) a
+  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat instLTNat (Fin.val n a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) h) a
 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_succ Fin.castLT_castSuccₓ'. -/
 @[simp]
 theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSucc a) h = a := by
@@ -1960,7 +1960,7 @@ theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (cast
 lean 3 declaration is
   forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) b)) (LT.lt.{0} (Fin n) (Fin.hasLt n) a b)
 but is expected to have type
-  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) b)) (LT.lt.{0} (Fin n) (instLTFin n) a b)
+  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) b)) (LT.lt.{0} (Fin n) (instLTFin n) a b)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_cast_succ_iff Fin.castSucc_lt_castSucc_iffₓ'. -/
 @[simp]
 theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
@@ -1971,7 +1971,7 @@ theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
 lean 3 declaration is
   forall (n : Nat), Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n))
 but is expected to have type
-  forall (n : Nat), Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n))
+  forall (n : Nat), Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_injective Fin.castSucc_injectiveₓ'. -/
 theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
   (castSucc : Fin n ↪o _).Injective
@@ -1981,7 +1981,7 @@ theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) b)) (Eq.{1} (Fin n) a b)
 but is expected to have type
-  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) b)) (Eq.{1} (Fin n) a b)
+  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) b)) (Eq.{1} (Fin n) a b)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_inj Fin.castSucc_injₓ'. -/
 theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
   (castSucc_injective n).eq_iff
@@ -1991,7 +1991,7 @@ theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
 lean 3 declaration is
   forall {n : Nat} (a : Fin n), LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (Fin.last n)
 but is expected to have type
-  forall {n : Nat} (a : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (Fin.last n)
+  forall {n : Nat} (a : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (Fin.last n)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_last Fin.castSucc_lt_lastₓ'. -/
 theorem castSucc_lt_last (a : Fin n) : castSucc a < last n :=
   lt_iff_val_lt_val.mpr a.is_lt
@@ -2001,7 +2001,7 @@ theorem castSucc_lt_last (a : Fin n) : castSucc a < last n :=
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n], Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n], Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n], Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_zero Fin.castSucc_zeroₓ'. -/
 @[simp]
 theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
@@ -2012,7 +2012,7 @@ theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
 lean 3 declaration is
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(One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne)) (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_one Fin.castSucc_oneₓ'. -/
 @[simp]
 theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
@@ -2023,7 +2023,7 @@ theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {i : Fin n}, (LT.lt.{0} (Fin n) (Fin.hasLt n) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))) i) -> (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {i : Fin n}, (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {i : Fin n}, (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_pos Fin.castSucc_posₓ'. -/
 /-- `cast_succ i` is positive when `i` is positive -/
 theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
@@ -2034,7 +2034,7 @@ theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (a : Fin n), Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Eq.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iffₓ'. -/
 @[simp]
 theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
@@ -2045,7 +2045,7 @@ theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (a : Fin n), Iff (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Ne.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Ne.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Ne.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iffₓ'. -/
 theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
   not_iff_not.mpr <| castSucc_eq_zero_iff a
@@ -2055,7 +2055,7 @@ theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a 
 lean 3 declaration is
   forall (n : Nat) (j : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (Nat.succ n)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (Nat.succ n)) (Fin.succ n j)) (Fin.succ (Nat.succ n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) j))
 but is expected to have type
-  forall (n : Nat) (j : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ n j)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (Nat.succ n)) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) j))
+  forall (n : Nat) (j : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ n j)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc (Nat.succ n)) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) j))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_fin_succ Fin.castSucc_fin_succₓ'. -/
 theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.succ (castSucc j) := by
   simp [Fin.ext_iff]
@@ -2065,7 +2065,7 @@ theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.su
 lean 3 declaration is
   forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HasLiftT.mk.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (CoeTCₓ.coe.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeTrans.{1, 1, 1} (Fin n) Nat (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Nat.castCoe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.addMonoidWithOne (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (NeZero.succ n)))) (Fin.coeToNat n)))) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a)
 but is expected to have type
-  forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) (Fin.val n a)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a)
+  forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) (Fin.val n a)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a)
 Case conversion may be inaccurate. Consider using '#align fin.coe_eq_cast_succ Fin.coe_eq_castSuccₓ'. -/
 @[norm_cast, simp]
 theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
@@ -2078,7 +2078,7 @@ theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HAdd.hAdd.{0, 0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (instHAdd.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasAdd (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.succ n a)
 but is expected to have type
-  forall {n : Nat} {a : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instHAdd.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (Fin.instAddFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 1 (NeZero.succ n)))) (Fin.succ n a)
+  forall {n : Nat} {a : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instHAdd.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (Fin.instAddFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 1 (NeZero.succ n)))) (Fin.succ n a)
 Case conversion may be inaccurate. Consider using '#align fin.coe_succ_eq_succ Fin.coeSucc_eq_succₓ'. -/
 @[simp]
 theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
@@ -2092,7 +2092,7 @@ theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n}, LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (Fin.succ n a)
 but is expected to have type
-  forall {n : Nat} {a : Fin n}, LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (Fin.succ n a)
+  forall {n : Nat} {a : Fin n}, LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) a) (Fin.succ n a)
 Case conversion may be inaccurate. Consider using '#align fin.lt_succ Fin.lt_succₓ'. -/
 theorem lt_succ : a.cast_succ < a.succ :=
   by
@@ -2104,7 +2104,7 @@ theorem lt_succ : a.cast_succ < a.succ :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n))) (setOf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) i) n))
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n))) (setOf.{0} (Fin (Nat.succ n)) (fun (i : Fin (Nat.succ n)) => LT.lt.{0} Nat instLTNat (Fin.val (Nat.succ n) i) n))
+  forall {n : Nat}, Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n))) (setOf.{0} (Fin (Nat.succ n)) (fun (i : Fin (Nat.succ n)) => LT.lt.{0} Nat instLTNat (Fin.val (Nat.succ n) i) n))
 Case conversion may be inaccurate. Consider using '#align fin.range_cast_succ Fin.range_castSuccₓ'. -/
 @[simp]
 theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = { i | (i : ℕ) < n } :=
@@ -2115,7 +2115,7 @@ theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) =
 lean 3 declaration is
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(One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) 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n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n)))) i hi))) (Fin.val (Nat.succ n) i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
@@ -2129,7 +2129,7 @@ theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (Nat.succ n)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i))
+  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_cast_succ Fin.succ_castSuccₓ'. -/
 theorem succ_castSucc {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
   Fin.ext (by simp)
@@ -2147,7 +2147,7 @@ def addNat (m) : Fin n ↪o Fin (n + m) :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i) m)
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) m)
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) m)
 Case conversion may be inaccurate. Consider using '#align fin.coe_add_nat Fin.coe_addNatₓ'. -/
 @[simp]
 theorem coe_addNat (m : ℕ) (i : Fin n) : (addNat m i : ℕ) = i + m :=
@@ -2158,7 +2158,7 @@ theorem coe_addNat (m : ℕ) (i : Fin n) : (addNat m i : ℕ) = i + m :=
 lean 3 declaration is
   forall {n : Nat} {i : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.addNat n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i) (Fin.succ n i)
 but is expected to have type
-  forall {n : Nat} {i : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (Fin.succ n i)
+  forall {n : Nat} {i : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_one Fin.addNat_oneₓ'. -/
 @[simp]
 theorem addNat_one {i : Fin n} : addNat 1 i = i.succ :=
@@ -2171,7 +2171,7 @@ theorem addNat_one {i : Fin n} : addNat 1 i = i.succ :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i))
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i))
+  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m) i))
 Case conversion may be inaccurate. Consider using '#align fin.le_coe_add_nat Fin.le_coe_addNatₓ'. -/
 theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNat m i :=
   Nat.le_add_left _ _
@@ -2181,7 +2181,7 @@ theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNat m i :=
 lean 3 declaration is
   forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat Nat.hasLt i m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.addNat m n) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n) (add_lt_add_right.{0} Nat Nat.hasAdd Nat.hasLt (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 but is expected to have type
-  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat m n) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n) (add_lt_add_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
+  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat m n) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n) (add_lt_add_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_mk Fin.addNat_mkₓ'. -/
 @[simp]
 theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, add_lt_add_right hi n⟩ :=
@@ -2192,7 +2192,7 @@ theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, ad
 lean 3 declaration is
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 but is expected to have type
-  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) n'), Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun 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(RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n (add_zero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_zero Fin.cast_addNat_zeroₓ'. -/
 @[simp]
 theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
@@ -2204,7 +2204,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8777 : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n h) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n' m) i))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2216,7 +2216,7 @@ theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n (add_right_cancel.{0} Nat Nat.hasAdd (AddRightCancelSemigroup.toIsRightCancelAdd.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) n' m n h)) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun 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(instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n (add_right_cancel.{0} Nat instAddNat (IsCancelAdd.toIsRightCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n' m n h)) i))
+  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n' m) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n' n (add_right_cancel.{0} Nat instAddNat (IsCancelAdd.toIsRightCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n' m n h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_left Fin.cast_addNat_leftₓ'. -/
 theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (addNat m i) = addNat m (cast (add_right_cancel h) i) :=
@@ -2227,7 +2227,7 @@ theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')))) (Fin.addNat n m') i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun 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(x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m') i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_right Fin.cast_addNat_rightₓ'. -/
 @[simp]
 theorem cast_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
@@ -2247,7 +2247,7 @@ def natAdd (n) {m} : Fin m ↪o Fin (n + m) :=
 lean 3 declaration is
   forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) i))
 but is expected to have type
-  forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (Fin.val m i))
+  forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (Fin.val m i))
 Case conversion may be inaccurate. Consider using '#align fin.coe_nat_add Fin.coe_natAddₓ'. -/
 @[simp]
 theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAdd n i : ℕ) = n + i :=
@@ -2258,7 +2258,7 @@ theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAdd n i : ℕ) = n + i
 lean 3 declaration is
   forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat Nat.hasLt i m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n i) (add_lt_add_left.{0} Nat Nat.hasAdd Nat.hasLt (AddLeftCancelSemigroup.covariant_add_lt_of_covariant_add_le.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 but is expected to have type
-  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd n m) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n i) (add_lt_add_left.{0} Nat instAddNat instLTNat (AddLeftCancelSemigroup.covariant_add_lt_of_covariant_add_le.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
+  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd n m) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n i) (add_lt_add_left.{0} Nat instAddNat instLTNat (AddLeftCancelSemigroup.covariant_add_lt_of_covariant_add_le.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_mk Fin.natAdd_mkₓ'. -/
 @[simp]
 theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAdd n ⟨i, hi⟩ = ⟨n + i, add_lt_add_left hi n⟩ :=
@@ -2269,7 +2269,7 @@ theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAdd n ⟨i, hi⟩ = ⟨n + i, ad
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i))
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i))
+  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i))
 Case conversion may be inaccurate. Consider using '#align fin.le_coe_nat_add Fin.le_coe_natAddₓ'. -/
 theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAdd m i :=
   Nat.le_add_right _ _
@@ -2279,7 +2279,7 @@ theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAdd m i :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n))) (Fin.cast n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n) (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n))))
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n))))
+  forall {n : Nat}, Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (Fin.cast n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n))))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_zero Fin.natAdd_zeroₓ'. -/
 theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRelEmbedding :=
   by
@@ -2291,7 +2291,7 @@ theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRe
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) (Fin.natAdd m n') i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8777 : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n h) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun 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x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n' n h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (congr_arg.{1, 1} Nat Nat n' n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m) h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n') i))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast Fin.natAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
 theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2303,7 +2303,7 @@ theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) (Fin.natAdd m n') i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n (add_left_cancel.{0} Nat Nat.hasAdd (AddLeftCancelSemigroup.toIsLeftCancelAdd.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n' n h)) i))
 but is expected to have type
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(instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (Fin 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n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n') i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n' n (add_left_cancel.{0} Nat instAddNat (IsCancelAdd.toIsLeftCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n' n h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_right Fin.cast_natAdd_rightₓ'. -/
 theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
     cast h (natAdd m i) = natAdd m (cast (add_left_cancel h) i) :=
@@ -2314,7 +2314,7 @@ theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
 lean 3 declaration is
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 but is expected to have type
-  forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m' n) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m' n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m' n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m' n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m' n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m' n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun 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(RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_left Fin.cast_natAdd_leftₓ'. -/
 @[simp]
 theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
@@ -2326,7 +2326,7 @@ theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
 lean 3 declaration is
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Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) n p))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m n) p))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) n p))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m n) p)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat Nat.addSemigroup)) n p))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} 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x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd n p) i)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_add Fin.castAdd_natAddₓ'. -/
 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     castAdd p (natAdd m i) = cast (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
@@ -2337,7 +2337,7 @@ theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
 lean 3 declaration is
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instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast_add Fin.natAdd_castAddₓ'. -/
 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     natAdd m (castAdd p i) = cast (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
@@ -2348,7 +2348,7 @@ theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.nat_add_nat_add Fin.natAdd_natAddₓ'. -/
 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
     natAdd m (natAdd n i) = cast (add_assoc _ _ _) (natAdd (m + n) i) :=
@@ -2359,7 +2359,7 @@ theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) n'), Eq.{1} (Fin n') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin n') (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin n') (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) n' h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) n'), Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) n' h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
+  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) n'), Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) n' h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_zero Fin.cast_natAdd_zeroₓ'. -/
 @[simp]
 theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
@@ -2371,7 +2371,7 @@ theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
 lean 3 declaration is
   forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n) (add_comm.{0} Nat Nat.addCommSemigroup n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.addNat m n) i)
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add Fin.cast_natAddₓ'. -/
 @[simp]
 theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAdd n i) = addNat n i :=
@@ -2382,7 +2382,7 @@ theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAd
 lean 3 declaration is
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(AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat 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(Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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 but is expected to have type
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(instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat Fin.cast_addNatₓ'. -/
 @[simp]
 theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNat m i) = natAdd m i :=
@@ -2393,7 +2393,7 @@ theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNa
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.nat_add_last Fin.natAdd_lastₓ'. -/
 @[simp]
 theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
@@ -2404,7 +2404,7 @@ theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
 lean 3 declaration is
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x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd n m) i))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast_succ Fin.natAdd_castSuccₓ'. -/
 theorem natAdd_castSucc {m n : ℕ} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
   rfl
@@ -2565,7 +2565,7 @@ theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
 lean 3 declaration is
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+  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.pred (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat 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Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i)) (ne_of_gt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i)) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.castSucc_pos (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n) (Fin.succ n i) (Fin.succ_pos n i)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)
 Case conversion may be inaccurate. Consider using '#align fin.pred_cast_succ_succ Fin.pred_castSucc_succₓ'. -/
 @[simp]
 theorem pred_castSucc_succ (i : Fin n) :
@@ -2577,7 +2577,7 @@ theorem pred_castSucc_succ (i : Fin n) :
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)} (h : LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) i)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (Fin.subNat n m i h)) i
 but is expected to have type
-  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat n m i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) (Fin.subNat n m i h)) i
+  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat n m i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m) (Fin.subNat n m i h)) i
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_sub_nat Fin.addNat_subNatₓ'. -/
 @[simp]
 theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat m (subNat m i h) = i :=
@@ -2588,7 +2588,7 @@ theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat m (subNat m i h)
 lean 3 declaration is
   forall {n : Nat} (i : Fin n) (m : Nat) (h : optParam.{0} (LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i))) (Fin.le_coe_addNat n m i)), Eq.{1} (Fin n) (Fin.subNat n m (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i) h) i
 but is expected to have type
-  forall {n : Nat} (i : Fin n) (m : Nat) (h : optParam.{0} (LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i))) (Fin.le_coe_addNat n m i)), Eq.{1} (Fin n) (Fin.subNat n m (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i) h) i
+  forall {n : Nat} (i : Fin n) (m : Nat) (h : optParam.{0} (LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m) i))) (Fin.le_coe_addNat n m i)), Eq.{1} (Fin n) (Fin.subNat n m (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.addNat n m) i) h) i
 Case conversion may be inaccurate. Consider using '#align fin.sub_nat_add_nat Fin.subNat_addNatₓ'. -/
 @[simp]
 theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addNat m i) :
@@ -2600,7 +2600,7 @@ theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addN
 lean 3 declaration is
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(Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) (Fin.subNat m n (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n) (add_comm.{0} Nat Nat.addCommSemigroup n m)) i) h)) i
 but is expected to have type
-  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat n (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat m n (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat 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x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n) (add_comm.{0} Nat Nat.addCommSemigroup n m)) i) h)) i
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castₓ'. -/
 @[simp]
 theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
@@ -2711,7 +2711,7 @@ theorem succRecOn_succ {C : ∀ n, Fin n → Sort _} {H0 Hs} {n} (i : Fin n) :
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), C i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
 Case conversion may be inaccurate. Consider using '#align fin.induction Fin.inductionₓ'. -/
 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
@@ -2731,7 +2731,7 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.induction.{u1} n C h0 hs (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13327 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13327) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13327 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13327) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
 Case conversion may be inaccurate. Consider using '#align fin.induction_zero Fin.induction_zeroₓ'. -/
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2743,7 +2743,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) (Fin.induction.{u1} n C h0 hs (Fin.succ n i)) (hs i (Fin.induction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
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Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2755,7 +2755,7 @@ theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (C i)
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (C i)
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (C i)
 Case conversion may be inaccurate. Consider using '#align fin.induction_on Fin.inductionOnₓ'. -/
 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
@@ -2893,7 +2893,7 @@ theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b :=
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), (C (Fin.succ n i)) -> (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), C i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
 Case conversion may be inaccurate. Consider using '#align fin.reverse_induction Fin.reverseInductionₓ'. -/
 /--
 Define `C i` by reverse induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
@@ -2919,7 +2919,7 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))), Eq.{u1} ((fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) (Fin.last n)) (Fin.reverseInduction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (Fin.last n)) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))), Eq.{u1} (C (Fin.last n)) (Fin.reverseInduction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) h0 hs (Fin.last n)) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i))), Eq.{u1} (C (Fin.last n)) (Fin.reverseInduction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) h0 hs (Fin.last n)) h0
 Case conversion may be inaccurate. Consider using '#align fin.reverse_induction_last Fin.reverse_induction_lastₓ'. -/
 @[simp]
 theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
@@ -2932,7 +2932,7 @@ theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (F
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) 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(instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (hs i (Fin.reverseInduction.{u1} n (fun (_x : Fin (Nat.succ n)) => C _x) h0 hs (Fin.succ n i)))
 but is expected to have type
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+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i))) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (Fin.reverseInduction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (hs i (Fin.reverseInduction.{u1} n (fun (_x : Fin (Nat.succ n)) => C _x) h0 hs (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSuccₓ'. -/
 @[simp]
 theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
@@ -2948,7 +2948,7 @@ theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 :
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), C i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
 Case conversion may be inaccurate. Consider using '#align fin.last_cases Fin.lastCasesₓ'. -/
 /-- Define `f : Π i : fin n.succ, C i` by separately handling the cases `i = fin.last n` and
 `i = j.cast_succ`, `j : fin n`. -/
@@ -2962,7 +2962,7 @@ def lastCases {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)), Eq.{u1} ((fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) (Fin.last n)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) hlast hcast (Fin.last n)) hlast
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)), Eq.{u1} (C (Fin.last n)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) hlast hcast (Fin.last n)) hlast
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)), Eq.{u1} (C (Fin.last n)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) hlast hcast (Fin.last n)) hlast
 Case conversion may be inaccurate. Consider using '#align fin.last_cases_last Fin.lastCases_lastₓ'. -/
 @[simp]
 theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
@@ -2975,7 +2975,7 @@ theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.la
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (i : Fin n), Eq.{u1} ((fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) hlast hcast (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (hcast i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (Fin.lastCases.{u1} n C hlast hcast (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin 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(Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (hcast i)
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 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(RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (Fin.lastCases.{u1} n C hlast hcast (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (hcast i)
 Case conversion may be inaccurate. Consider using '#align fin.last_cases_cast_succ Fin.lastCases_castSuccₓ'. -/
 @[simp]
 theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
@@ -2988,7 +2988,7 @@ theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fi
 lean 3 declaration is
   forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) -> Sort.{u1}}, (forall (i : Fin m), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) -> (forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)), C i)
 but is expected to have type
-  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}}, (forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)), C i)
+  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}}, (forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd m n) i)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)), C i)
 Case conversion may be inaccurate. Consider using '#align fin.add_cases Fin.addCasesₓ'. -/
 /-- Define `f : Π i : fin (m + n), C i` by separately handling the cases `i = cast_add n i`,
 `j : fin m` and `i = nat_add m j`, `j : fin n`. -/
@@ -3003,7 +3003,7 @@ def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd
 lean 3 declaration is
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 but is expected to have type
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Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i)) (i : Fin m), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd m n) i)) (Fin.addCases.{u1} m n C hleft hright (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd m n) i)) (hleft i)
 Case conversion may be inaccurate. Consider using '#align fin.add_cases_left Fin.addCases_leftₓ'. -/
 @[simp]
 theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
@@ -3019,7 +3019,7 @@ theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C
 lean 3 declaration is
   forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) (hright : forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) (i : Fin n), Eq.{u1} (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) (Fin.addCases.{u1} m n C hleft hright (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) (hright i)
 but is expected to have type
-  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) (hright : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) 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(OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat 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+  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castAdd m n) i)) (hright : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 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Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) 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instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.natAdd m n) i)) (hright i)
 Case conversion may be inaccurate. Consider using '#align fin.add_cases_right Fin.addCases_rightₓ'. -/
 @[simp]
 theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
@@ -3039,7 +3039,7 @@ end Rec
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α α (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) r f f) (forall (i : Fin n), r (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15357 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15359 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15357 x._@.Mathlib.Data.Fin.Basic._hyg.15359) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15357 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15359 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15357 x._@.Mathlib.Data.Fin.Basic._hyg.15359) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=
@@ -3059,7 +3059,7 @@ theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r]
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.strict_mono_iff_lt_succ Fin.strictMono_iff_lt_succₓ'. -/
 /-- A function `f` on `fin (n + 1)` is strictly monotone if and only if `f i < f (i + 1)`
 for all `i`. -/
@@ -3072,7 +3072,7 @@ theorem strictMono_iff_lt_succ {α : Type _} [Preorder α] {f : Fin (n + 1) →
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.monotone_iff_le_succ Fin.monotone_iff_le_succₓ'. -/
 /-- A function `f` on `fin (n + 1)` is monotone if and only if `f i ≤ f (i + 1)` for all `i`. -/
 theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
@@ -3084,7 +3084,7 @@ theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.strict_anti_iff_succ_lt Fin.strictAnti_iff_succ_ltₓ'. -/
 /-- A function `f` on `fin (n + 1)` is strictly antitone if and only if `f (i + 1) < f i`
 for all `i`. -/
@@ -3097,7 +3097,7 @@ theorem strictAnti_iff_succ_lt {α : Type _} [Preorder α] {f : Fin (n + 1) →
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.antitone_iff_succ_le Fin.antitone_iff_succ_leₓ'. -/
 /-- A function `f` on `fin (n + 1)` is antitone if and only if `f (i + 1) ≤ f i` for all `i`. -/
 theorem antitone_iff_succ_le {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
@@ -3268,7 +3268,7 @@ section SuccAbove
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), StrictMono.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (i : Fin n) => ite.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) (Fin.decidableLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), StrictMono.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (fun (i : Fin n) => ite.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_aux Fin.succAbove_auxₓ'. -/
 theorem succAbove_aux (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
@@ -3292,7 +3292,7 @@ def succAbove (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i) p) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_below Fin.succAbove_belowₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
@@ -3306,7 +3306,7 @@ theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zeroₓ'. -/
 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 :=
@@ -3320,7 +3320,7 @@ theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.s
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iffₓ'. -/
 theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) :
     a.succAbove b = 0 ↔ b = 0 := by
@@ -3331,7 +3331,7 @@ theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a 
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) -> (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) -> (Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) -> (Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne_zero Fin.succAbove_ne_zeroₓ'. -/
 theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) (hb : b ≠ 0) :
     a.succAbove b ≠ 0 :=
@@ -3342,7 +3342,7 @@ theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))) (Fin.succ n)
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (Fin.succ n)
+  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (Fin.succ n)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_zero Fin.succAbove_zeroₓ'. -/
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around zero embeds by `succ`. -/
 @[simp]
@@ -3368,7 +3368,7 @@ theorem succAbove_last : succAbove (Fin.last n) = castSucc :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.last n)) i) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (Fin.last n)) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)
+  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n (Fin.last n)) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_last_apply Fin.succAbove_last_applyₓ'. -/
 theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_succ := by
   rw [succ_above_last]
@@ -3378,7 +3378,7 @@ theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_suc
 lean 3 declaration is
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 but is expected to have type
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(instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n p) i) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_above Fin.succAbove_aboveₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
@@ -3390,7 +3390,7 @@ theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Or (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i) p) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_ge Fin.succAbove_lt_geₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p ≤ i.cast_succ :=
@@ -3401,7 +3401,7 @@ theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p 
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Or (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (Fin.succ n i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i) p) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_gt Fin.succAbove_lt_gtₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
@@ -3413,7 +3413,7 @@ theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p <
 lean 3 declaration is
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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n p) i) p) (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i) p)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_iff Fin.succAbove_lt_iffₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
@@ -3435,7 +3435,7 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n p) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.lt_succ_above_iff Fin.lt_succAbove_iffₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
@@ -3456,7 +3456,7 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) p
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i) p
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n p) i) p
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne Fin.succAbove_neₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 never results in `p` itself -/
@@ -3472,7 +3472,7 @@ theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LT.lt.{0} (Fin n) (Fin.hasLt n) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))) i) -> (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n p) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pos Fin.succAbove_posₓ'. -/
 /-- Embedding a positive `fin n` results in a positive fin (n + 1)` -/
 theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i :=
@@ -3486,7 +3486,7 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hx : optParam.{0} (LT.lt.{0} Nat (Preorder.toHasLt.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) y) n h (Fin.le_last n y))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x hx)) x
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hx : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n h (Fin.le_last n y))), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) x
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hx : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n h (Fin.le_last n y))), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) x
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_cast_lt Fin.succAbove_castLTₓ'. -/
 @[simp]
 theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
@@ -3500,7 +3500,7 @@ theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hy : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (LT.lt.ne'.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) y (LE.le.trans_lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat 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Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) (Fin.pred n y hy)) y
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hy : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (LT.lt.ne'.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin 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+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hy : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (LT.lt.ne'.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat 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(instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) x y (Fin.zero_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n) x) h))), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.pred n y hy)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin 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 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred Fin.succAbove_predₓ'. -/
 @[simp]
 theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
@@ -3514,7 +3514,7 @@ theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_
 lean 3 declaration is
   forall {n : Nat} {x : Fin n} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} 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(One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} 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(x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) x) y) (Fin.succAbove_lt_iff n y x) h) (Fin.le_last n y))), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat 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 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_succ_above Fin.castLT_succAboveₓ'. -/
 theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
     (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
@@ -3525,7 +3525,7 @@ theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above Fin.pred_succAboveₓ'. -/
 theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
     (h' : y.succAbove x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
@@ -3536,7 +3536,7 @@ theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) z) x))
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n y) z) x))
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n y) z) x))
 Case conversion may be inaccurate. Consider using '#align fin.exists_succ_above_eq Fin.exists_succAbove_eqₓ'. -/
 theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x :=
   by
@@ -3548,7 +3548,7 @@ theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbo
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y x)
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y x)
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y x)
 Case conversion may be inaccurate. Consider using '#align fin.exists_succ_above_eq_iff Fin.exists_succAbove_eq_iffₓ'. -/
 @[simp]
 theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y) ↔ y ≠ x :=
@@ -3562,7 +3562,7 @@ theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y)
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.booleanAlgebra.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.hasSingleton.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) p))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instBooleanAlgebraSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instSingletonSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) p))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n p))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instBooleanAlgebraSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instSingletonSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) p))
 Case conversion may be inaccurate. Consider using '#align fin.range_succ_above Fin.range_succAboveₓ'. -/
 /-- The range of `p.succ_above` is everything except `p`. -/
 @[simp]
@@ -3596,7 +3596,7 @@ theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x))
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x))
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n x))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_right_injective Fin.succAbove_right_injectiveₓ'. -/
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
@@ -3607,7 +3607,7 @@ theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
 but is expected to have type
-  forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
+  forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n x) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_right_inj Fin.succAbove_right_injₓ'. -/
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b ↔ a = b :=
@@ -3641,7 +3641,7 @@ theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAbove = y.succAbove ↔ x
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) i) (Fin.succ n i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) i) (Fin.succ n i)
+  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.zero_succ_above Fin.zero_succAboveₓ'. -/
 @[simp]
 theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i.succ :=
@@ -3652,7 +3652,7 @@ theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_zero Fin.succ_succAbove_zeroₓ'. -/
 @[simp]
 theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove 0 = 0 :=
@@ -3663,7 +3663,7 @@ theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove
 lean 3 declaration is
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Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n i) j))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_succ Fin.succ_succAbove_succₓ'. -/
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
@@ -3683,7 +3683,7 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> 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 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_zero Fin.one_succAbove_zeroₓ'. -/
 @[simp]
 theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
@@ -3694,7 +3694,7 @@ theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
 lean 3 declaration is
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(x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 1 (NeZero.succ n)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n i) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_one Fin.succ_succAbove_oneₓ'. -/
 /-- By moving `succ` to the outside of this expression, we create opportunities for further
 simplification using `succ_above_zero` or `succ_succ_above_zero`. -/
@@ -3708,7 +3708,7 @@ theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
 lean 3 declaration is
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Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))))))) (Fin.succ n j)) (Fin.succ (Nat.succ n) (Fin.succ n j))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_succ Fin.one_succAbove_succₓ'. -/
 @[simp]
 theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j.succ = j.succ.succ :=
@@ -3719,7 +3719,7 @@ theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j
 lean 3 declaration is
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(instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_one Fin.one_succAbove_oneₓ'. -/
 @[simp]
 theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 :=
@@ -3849,7 +3849,7 @@ theorem coe_castPred {n : ℕ} (a : Fin (n + 2)) (hx : a < Fin.last _) : (a.cast
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.pred_above_below Fin.predAbove_belowₓ'. -/
 theorem predAbove_below (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_succ) :
     p.predAbove i = i.cast_pred :=
@@ -3879,7 +3879,7 @@ theorem predAbove_last_apply (i : Fin n) : predAbove (Fin.last n) i = i.cast_pre
 lean 3 declaration is
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(Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 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 but is expected to have type
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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) p)) h))))
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_above Fin.predAbove_aboveₓ'. -/
 theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
     p.predAbove i = i.pred (p.cast_succ.zero_le.trans_lt h).Ne.symm := by simp [pred_above, h]
@@ -3899,7 +3899,7 @@ theorem castPred_monotone : Monotone (@castPred n) :=
 lean 3 declaration is
   forall {n : Nat} {p : Fin n} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) (Fin.predAbove n p i)) i)
 but is expected to have type
-  forall {n : Nat} {p : Fin n} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.predAbove n p i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) (Fin.predAbove n p i)) i)
+  forall {n : Nat} {p : Fin n} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) p)) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.predAbove n p i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc n) p)) (Fin.predAbove n p i)) i)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred_above Fin.succAbove_predAboveₓ'. -/
 /-- Sending `fin (n+1)` to `fin n` by subtracting one from anything above `p`
 then back to `fin (n+1)` with a gap around `p` is the identity away from `p`. -/
@@ -3932,7 +3932,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
 lean 3 declaration is
   forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) i)) i
 but is expected to have type
-  forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) i)) i
+  forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin 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 Case conversion may be inaccurate. Consider using '#align fin.pred_above_succ_above Fin.predAbove_succAboveₓ'. -/
 /-- Sending `fin n` into `fin (n + 1)` with a gap at `p`
 then back to `fin n` by subtracting one from anything above `p` is the identity. -/
@@ -3958,7 +3958,7 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
 lean 3 declaration is
   forall {n : Nat} {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (ha : Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (ha' : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 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 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSuccₓ'. -/
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
     (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' :=
@@ -3971,7 +3971,7 @@ theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above_pred Fin.pred_succAbove_predₓ'. -/
 /-- `pred` commutes with `succ_above`. -/
 theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
@@ -4022,7 +4022,7 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.castPred n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i)) i
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) i
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_pred_cast_succ Fin.castPred_castSuccₓ'. -/
 @[simp]
 theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
@@ -4033,7 +4033,7 @@ theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
 lean 3 declaration is
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Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.castPred n i)) i)
 but is expected to have type
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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n i)) i)
+  forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))}, (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) i (Fin.last (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n i)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_pred Fin.castSucc_castPredₓ'. -/
 theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSucc i.cast_pred = i :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -802,20 +802,28 @@ theorem coe_orderIso_apply (e : Fin n ≃o Fin m) (i : Fin n) : (e i : ℕ) = i
   · rwa [← h j hj (hj.trans hi), ← lt_iff_coe_lt_coe, e.lt_iff_lt]
 #align fin.coe_order_iso_apply Fin.coe_orderIso_apply
 
-#print Fin.orderIso_subsingleton /-
+/- warning: fin.order_iso_subsingleton -> Fin.orderIso_subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Subsingleton.{succ u1} (OrderIso.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1))
+but is expected to have type
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Subsingleton.{succ u1} (OrderIso.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align fin.order_iso_subsingleton Fin.orderIso_subsingletonₓ'. -/
 instance orderIso_subsingleton : Subsingleton (Fin n ≃o α) :=
   ⟨fun e e' => by
     ext i
     rw [← e.symm.apply_eq_iff_eq, e.symm_apply_apply, ← e'.trans_apply, ext_iff,
       coe_order_iso_apply]⟩
 #align fin.order_iso_subsingleton Fin.orderIso_subsingleton
--/
 
-#print Fin.orderIso_subsingleton' /-
+/- warning: fin.order_iso_subsingleton' -> Fin.orderIso_subsingleton' is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Subsingleton.{succ u1} (OrderIso.{u1, 0} α (Fin n) (Preorder.toHasLe.{u1} α _inst_1) (Fin.hasLe n))
+but is expected to have type
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Subsingleton.{succ u1} (OrderIso.{u1, 0} α (Fin n) (Preorder.toLE.{u1} α _inst_1) (instLEFin n))
+Case conversion may be inaccurate. Consider using '#align fin.order_iso_subsingleton' Fin.orderIso_subsingleton'ₓ'. -/
 instance orderIso_subsingleton' : Subsingleton (α ≃o Fin n) :=
   OrderIso.symm_injective.Subsingleton
 #align fin.order_iso_subsingleton' Fin.orderIso_subsingleton'
--/
 
 #print Fin.orderIsoUnique /-
 instance orderIsoUnique : Unique (Fin n ≃o Fin n) :=
@@ -839,7 +847,7 @@ theorem strictMono_unique {f g : Fin n → α} (hf : StrictMono f) (hg : StrictM
 
 /- warning: fin.order_embedding_eq -> Fin.orderEmbedding_eq is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) f)) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)) f g)
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) f)) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toHasLe.{u1} α _inst_1)) f g)
 but is expected to have type
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f)) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) f g)
 Case conversion may be inaccurate. Consider using '#align fin.order_embedding_eq Fin.orderEmbedding_eqₓ'. -/
@@ -1263,7 +1271,7 @@ theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by simp [lt_iff_coe
 
 /- warning: fin.succ_embedding -> Fin.succEmbedding is a dubious translation:
 lean 3 declaration is
-  forall (n : Nat), OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))
+  forall (n : Nat), OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))
 but is expected to have type
   forall (n : Nat), OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_embedding Fin.succEmbeddingₓ'. -/
@@ -1274,7 +1282,7 @@ def succEmbedding (n : ℕ) : Fin n ↪o Fin (n + 1) :=
 
 /- warning: fin.coe_succ_embedding -> Fin.val_succEmbedding is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succEmbedding n)) (Fin.succ n)
+  forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succEmbedding n)) (Fin.succ n)
 but is expected to have type
   forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succEmbedding n)) (Fin.succ n)
 Case conversion may be inaccurate. Consider using '#align fin.coe_succ_embedding Fin.val_succEmbeddingₓ'. -/
@@ -2541,13 +2549,17 @@ theorem coe_subNat (i : Fin (n + m)) (h : m ≤ i) : (i.subNat m h : ℕ) = i -
 #align fin.coe_sub_nat Fin.coe_subNat
 -/
 
-#print Fin.subNat_mk /-
+/- warning: fin.sub_nat_mk -> Fin.subNat_mk is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat} {m : Nat} {i : Nat} (h₁ : LT.lt.{0} Nat Nat.hasLt i (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (h₂ : LE.le.{0} Nat Nat.hasLe m i), Eq.{1} (Fin n) (Fin.subNat n m (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i h₁) h₂) (Fin.mk n (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i m) (Iff.mpr (LT.lt.{0} Nat (Preorder.toHasLt.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i m) n) (LT.lt.{0} Nat (Preorder.toHasLt.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) i (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (tsub_lt_iff_right.{0} Nat Nat.addCommSemigroup (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (CanonicallyOrderedAddMonoid.existsAddOfLE.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring)) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring)) Nat.hasSub Nat.orderedSub i m n (AddLeftCancelSemigroup.contravariant_add_le_of_contravariant_add_lt.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedCancelAddCommMonoid.to_contravariantClass_left.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) h₂) h₁))
+but is expected to have type
+  forall {n : Nat} {m : Nat} {i : Nat} (h₁ : LT.lt.{0} Nat instLTNat i (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (h₂ : LE.le.{0} Nat instLENat m i), Eq.{1} (Fin n) (Fin.subNat n m (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i h₁) h₂) (Fin.mk n (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i m) (Iff.mpr (LT.lt.{0} Nat (Preorder.toLT.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i m) n) (LT.lt.{0} Nat (Preorder.toLT.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) i (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (tsub_lt_iff_right.{0} Nat Nat.addCommSemigroup (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (CanonicallyOrderedAddMonoid.existsAddOfLE.{0} Nat (CanonicallyOrderedCommSemiring.toCanonicallyOrderedAddMonoid.{0} Nat Nat.canonicallyOrderedCommSemiring)) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring)) instSubNat Nat.instOrderedSubNatInstLENatInstAddNatInstSubNat i m n (AddLeftCancelSemigroup.contravariant_add_le_of_contravariant_add_lt.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedCancelAddCommMonoid.to_contravariantClass_left.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) h₂) h₁))
+Case conversion may be inaccurate. Consider using '#align fin.sub_nat_mk Fin.subNat_mkₓ'. -/
 @[simp]
 theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
     subNat m ⟨i, h₁⟩ h₂ = ⟨i - m, (tsub_lt_iff_right h₂).2 h₁⟩ :=
   rfl
 #align fin.sub_nat_mk Fin.subNat_mk
--/
 
 /- warning: fin.pred_cast_succ_succ -> Fin.pred_castSucc_succ is a dubious translation:
 lean 3 declaration is
@@ -3045,7 +3057,7 @@ theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r]
 
 /- warning: fin.strict_mono_iff_lt_succ -> Fin.strictMono_iff_lt_succ is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.strict_mono_iff_lt_succ Fin.strictMono_iff_lt_succₓ'. -/
@@ -3058,7 +3070,7 @@ theorem strictMono_iff_lt_succ {α : Type _} [Preorder α] {f : Fin (n + 1) →
 
 /- warning: fin.monotone_iff_le_succ -> Fin.monotone_iff_le_succ is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.monotone_iff_le_succ Fin.monotone_iff_le_succₓ'. -/
@@ -3070,7 +3082,7 @@ theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α
 
 /- warning: fin.strict_anti_iff_succ_lt -> Fin.strictAnti_iff_succ_lt is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.strict_anti_iff_succ_lt Fin.strictAnti_iff_succ_ltₓ'. -/
@@ -3083,7 +3095,7 @@ theorem strictAnti_iff_succ_lt {α : Type _} [Preorder α] {f : Fin (n + 1) →
 
 /- warning: fin.antitone_iff_succ_le -> Fin.antitone_iff_succ_le is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.antitone_iff_succ_le Fin.antitone_iff_succ_leₓ'. -/
@@ -3267,7 +3279,7 @@ theorem succAbove_aux (p : Fin (n + 1)) :
 
 /- warning: fin.succ_above -> Fin.succAbove is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+  forall {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
   forall {n : Nat}, (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above Fin.succAboveₓ'. -/
@@ -3278,7 +3290,7 @@ def succAbove (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
 
 /- warning: fin.succ_above_below -> Fin.succAbove_below is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin 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Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin 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(instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_below Fin.succAbove_belowₓ'. -/
@@ -3292,7 +3304,7 @@ theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
 
 /- warning: fin.succ_above_ne_zero_zero -> Fin.succAbove_ne_zero_zero is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
 but is expected to have type
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zeroₓ'. -/
@@ -3306,7 +3318,7 @@ theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.s
 
 /- warning: fin.succ_above_eq_zero_iff -> Fin.succAbove_eq_zero_iff is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))))
 but is expected to have type
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iffₓ'. -/
@@ -3317,7 +3329,7 @@ theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a 
 
 /- warning: fin.succ_above_ne_zero -> Fin.succAbove_ne_zero is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) -> (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) -> (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
 but is expected to have type
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) -> (Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne_zero Fin.succAbove_ne_zeroₓ'. -/
@@ -3328,7 +3340,7 @@ theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0
 
 /- warning: fin.succ_above_zero -> Fin.succAbove_zero is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))) (Fin.succ n)
+  forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))) (Fin.succ n)
 but is expected to have type
   forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (Fin.succ n)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_zero Fin.succAbove_zeroₓ'. -/
@@ -3340,7 +3352,7 @@ theorem succAbove_zero : ⇑(succAbove (0 : Fin (n + 1))) = Fin.succ :=
 
 /- warning: fin.succ_above_last -> Fin.succAbove_last is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat}, Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Fin.succAbove n (Fin.last n)) (Fin.castSucc n)
+  forall {n : Nat}, Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Fin.succAbove n (Fin.last n)) (Fin.castSucc n)
 but is expected to have type
   forall {n : Nat}, Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.succAbove n (Fin.last n)) (Fin.castSucc n)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_last Fin.succAbove_lastₓ'. -/
@@ -3354,7 +3366,7 @@ theorem succAbove_last : succAbove (Fin.last n) = castSucc :=
 
 /- warning: fin.succ_above_last_apply -> Fin.succAbove_last_apply is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.last n)) i) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)
+  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.last n)) i) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)
 but is expected to have type
   forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (Fin.last n)) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_last_apply Fin.succAbove_last_applyₓ'. -/
@@ -3364,7 +3376,7 @@ theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_suc
 
 /- warning: fin.succ_above_above -> Fin.succAbove_above is a dubious translation:
 lean 3 declaration is
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+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) (Fin.succ n i))
 but is expected to have type
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_above Fin.succAbove_aboveₓ'. -/
@@ -3399,7 +3411,7 @@ theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p <
 
 /- warning: fin.succ_above_lt_iff -> Fin.succAbove_lt_iff is a dubious translation:
 lean 3 declaration is
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(OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p)
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 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Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) p) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p)
 but is expected to have type
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i) p) (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_iff Fin.succAbove_lt_iffₓ'. -/
@@ -3421,7 +3433,7 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
 
 /- warning: fin.lt_succ_above_iff -> Fin.lt_succAbove_iff is a dubious translation:
 lean 3 declaration is
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(OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 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Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.lt_succ_above_iff Fin.lt_succAbove_iffₓ'. -/
@@ -3442,7 +3454,7 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
 
 /- warning: fin.succ_above_ne -> Fin.succAbove_ne is a dubious translation:
 lean 3 declaration is
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+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) p
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne Fin.succAbove_neₓ'. -/
@@ -3458,7 +3470,7 @@ theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
 
 /- warning: fin.succ_above_pos -> Fin.succAbove_pos is a dubious translation:
 lean 3 declaration is
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+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LT.lt.{0} (Fin n) (Fin.hasLt n) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))) i) -> (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i))
 but is expected to have type
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pos Fin.succAbove_posₓ'. -/
@@ -3472,7 +3484,7 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
 
 /- warning: fin.succ_above_cast_lt -> Fin.succAbove_castLT is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hx : optParam.{0} (LT.lt.{0} Nat (Preorder.toLT.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) y) n h (Fin.le_last n y))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x hx)) x
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hx : optParam.{0} (LT.lt.{0} Nat (Preorder.toHasLt.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) y) n h (Fin.le_last n y))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x hx)) x
 but is expected to have type
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hx : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n h (Fin.le_last n y))), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) x
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_cast_lt Fin.succAbove_castLTₓ'. -/
@@ -3486,7 +3498,7 @@ theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
 
 /- warning: fin.succ_above_pred -> Fin.succAbove_pred is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hy : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} 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 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred Fin.succAbove_predₓ'. -/
@@ -3500,7 +3512,7 @@ theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_
 
 /- warning: fin.cast_lt_succ_above -> Fin.castLT_succAbove is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_succ_above Fin.castLT_succAboveₓ'. -/
@@ -3511,7 +3523,7 @@ theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
 
 /- warning: fin.pred_succ_above -> Fin.pred_succAbove is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above Fin.pred_succAboveₓ'. -/
@@ -3522,7 +3534,7 @@ theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
 
 /- warning: fin.exists_succ_above_eq -> Fin.exists_succAbove_eq is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) z) x))
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) z) x))
 but is expected to have type
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n y) z) x))
 Case conversion may be inaccurate. Consider using '#align fin.exists_succ_above_eq Fin.exists_succAbove_eqₓ'. -/
@@ -3534,7 +3546,7 @@ theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbo
 
 /- warning: fin.exists_succ_above_eq_iff -> Fin.exists_succAbove_eq_iff is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y x)
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y x)
 but is expected to have type
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y x)
 Case conversion may be inaccurate. Consider using '#align fin.exists_succ_above_eq_iff Fin.exists_succAbove_eq_iffₓ'. -/
@@ -3548,7 +3560,7 @@ theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y)
 
 /- warning: fin.range_succ_above -> Fin.range_succAbove is a dubious translation:
 lean 3 declaration is
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+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.booleanAlgebra.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.hasSingleton.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) p))
 but is expected to have type
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instBooleanAlgebraSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instSingletonSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) p))
 Case conversion may be inaccurate. Consider using '#align fin.range_succ_above Fin.range_succAboveₓ'. -/
@@ -3582,7 +3594,7 @@ theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠
 
 /- warning: fin.succ_above_right_injective -> Fin.succAbove_right_injective is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x))
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x))
 but is expected to have type
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_right_injective Fin.succAbove_right_injectiveₓ'. -/
@@ -3593,7 +3605,7 @@ theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
 
 /- warning: fin.succ_above_right_inj -> Fin.succAbove_right_inj is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
+  forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
 but is expected to have type
   forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_right_inj Fin.succAbove_right_injₓ'. -/
@@ -3604,7 +3616,7 @@ theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b 
 
 /- warning: fin.succ_above_left_injective -> Fin.succAbove_left_injective is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat}, Function.Injective.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Fin.succAbove n)
+  forall {n : Nat}, Function.Injective.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Fin.succAbove n)
 but is expected to have type
   forall {n : Nat}, Function.Injective.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.succAbove n)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_left_injective Fin.succAbove_left_injectiveₓ'. -/
@@ -3615,7 +3627,7 @@ theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
 
 /- warning: fin.succ_above_left_inj -> Fin.succAbove_left_inj is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Fin.succAbove n x) (Fin.succAbove n y)) (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y)
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Fin.succAbove n x) (Fin.succAbove n y)) (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y)
 but is expected to have type
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Eq.{1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.succAbove n x) (Fin.succAbove n y)) (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_left_inj Fin.succAbove_left_injₓ'. -/
@@ -3627,7 +3639,7 @@ theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAbove = y.succAbove ↔ x
 
 /- warning: fin.zero_succ_above -> Fin.zero_succAbove is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) i) (Fin.succ n i)
+  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) i) (Fin.succ n i)
 but is expected to have type
   forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.zero_succ_above Fin.zero_succAboveₓ'. -/
@@ -3638,7 +3650,7 @@ theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i
 
 /- warning: fin.succ_succ_above_zero -> Fin.succ_succAbove_zero is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))
 but is expected to have type
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_zero Fin.succ_succAbove_zeroₓ'. -/
@@ -3649,7 +3661,7 @@ theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove
 
 /- warning: fin.succ_succ_above_succ -> Fin.succ_succAbove_succ is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (j : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} 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Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat 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 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_succ Fin.succ_succAbove_succₓ'. -/
@@ -3669,7 +3681,7 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
 
 /- warning: fin.one_succ_above_zero -> Fin.one_succAbove_zero is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_zero Fin.one_succAbove_zeroₓ'. -/
@@ -3680,7 +3692,7 @@ theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
 
 /- warning: fin.succ_succ_above_one -> Fin.succ_succAbove_one is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_one Fin.succ_succAbove_oneₓ'. -/
@@ -3694,7 +3706,7 @@ theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
 
 /- warning: fin.one_succ_above_succ -> Fin.one_succAbove_succ is a dubious translation:
 lean 3 declaration is
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(Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_succ Fin.one_succAbove_succₓ'. -/
@@ -3705,7 +3717,7 @@ theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j
 
 /- warning: fin.one_succ_above_one -> Fin.one_succAbove_one is a dubious translation:
 lean 3 declaration is
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Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
 but is expected to have type
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(instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 1 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) 2 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 2 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_one Fin.one_succAbove_oneₓ'. -/
@@ -3885,7 +3897,7 @@ theorem castPred_monotone : Monotone (@castPred n) :=
 
 /- warning: fin.succ_above_pred_above -> Fin.succAbove_predAbove is a dubious translation:
 lean 3 declaration is
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x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.predAbove n p i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) (Fin.predAbove n p i)) i)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred_above Fin.succAbove_predAboveₓ'. -/
@@ -3918,7 +3930,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
 
 /- warning: fin.pred_above_succ_above -> Fin.predAbove_succAbove is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) i)) i
+  forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) i)) i
 but is expected to have type
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(instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) i)) i
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_succ_above Fin.predAbove_succAboveₓ'. -/
@@ -3957,7 +3969,7 @@ theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
 
 /- warning: fin.pred_succ_above_pred -> Fin.pred_succAbove_pred is a dubious translation:
 lean 3 declaration is
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0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))))))) (hb : Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) b (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hk : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above_pred Fin.pred_succAbove_predₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -1683,7 +1683,7 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (Fin.cast n m h)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h)) (cast.{1} (Fin n) (Fin m) (Eq.subst.{1} Nat (fun (_x : Nat) => Eq.{2} Type (Fin n) (Fin _x)) n m h (rfl.{2} Type (Fin n))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((Fin n) -> (Fin m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8776 : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8319 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8320 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8319) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8319) (rfl.{1} Nat n) m h)))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((Fin n) -> (Fin m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8777 : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8320 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8321 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8320) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8320) (rfl.{1} Nat n) m h)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
@@ -1770,7 +1770,7 @@ theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i))
 but is expected to have type
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(x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8624 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8624 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (n' : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n' m) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2196,7 +2196,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8776 : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n h) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n' m) i))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2283,7 +2283,7 @@ theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRe
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) (Fin.natAdd m n') i))
 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n h) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun 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x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n') i))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast Fin.natAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
 theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2588,7 +2588,7 @@ theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addN
 lean 3 declaration is
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(Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) (Fin.subNat m n (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n) (add_comm.{0} Nat Nat.addCommSemigroup n m)) i) h)) i
 but is expected to have type
-  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat n (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat m n (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8776 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat 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x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 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 Case conversion may be inaccurate. Consider using '#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castₓ'. -/
 @[simp]
 theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
@@ -2719,7 +2719,7 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.induction.{u1} n C h0 hs (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13326 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13326) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13327 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13327) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
 Case conversion may be inaccurate. Consider using '#align fin.induction_zero Fin.induction_zeroₓ'. -/
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2731,7 +2731,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) (Fin.induction.{u1} n C h0 hs (Fin.succ n i)) (hs i (Fin.induction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
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Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -3027,7 +3027,7 @@ end Rec
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α α (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) r f f) (forall (i : Fin n), r (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15356 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15358 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15356 x._@.Mathlib.Data.Fin.Basic._hyg.15358) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15357 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15359 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15357 x._@.Mathlib.Data.Fin.Basic._hyg.15359) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=
@@ -3651,7 +3651,7 @@ theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (j : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun 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Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n i) j))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_succ Fin.succ_succAbove_succₓ'. -/
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
@@ -3682,7 +3682,7 @@ theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
 lean 3 declaration is
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0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 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(Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun 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x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 1 (NeZero.succ n)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n i) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_one Fin.succ_succAbove_oneₓ'. -/
 /-- By moving `succ` to the outside of this expression, we create opportunities for further
 simplification using `succ_above_zero` or `succ_succ_above_zero`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -695,7 +695,7 @@ def revOrderIso {n} : (Fin n)ᵒᵈ ≃o Fin n :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (OrderDual.{0} (Fin n)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (Fin.hasLe n) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n))) (fun (_x : RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)))) => (Fin n) -> (OrderDual.{0} (Fin n))) (RelIso.hasCoeToFun.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)))) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)) (Fin.hasLe n) (Fin.revOrderIso n)) i) (coeFn.{1, 1} (Equiv.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (fun (_x : Equiv.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) => (Fin n) -> (OrderDual.{0} (Fin n))) (Equiv.hasCoeToFun.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (OrderDual.toDual.{0} (Fin n)) (coeFn.{1, 1} (Equiv.Perm.{1} (Fin n)) (fun (_x : Equiv.{1, 1} (Fin n) (Fin n)) => (Fin n) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => OrderDual.{0} (Fin n)) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => OrderDual.{0} (Fin n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (Fin n) (OrderDual.{0} (Fin n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) (instLEFin n) (Fin.revOrderIso n)))) i) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (fun (_x : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) _x) (Equiv.instFunLikeEquiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) (OrderDual.toDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
+  forall {n : Nat} (i : Fin n), Eq.{1} (OrderDual.{0} (Fin n)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => OrderDual.{0} (Fin n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) (instLEFin n) (Fin.revOrderIso n)) i) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (fun (_x : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) _x) (Equiv.instFunLikeEquiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) (OrderDual.toDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
 Case conversion may be inaccurate. Consider using '#align fin.rev_order_iso_symm_apply Fin.revOrderIso_symm_applyₓ'. -/
 @[simp]
 theorem revOrderIso_symm_apply (i : Fin n) : revOrderIso.symm i = OrderDual.toDual i.rev :=
@@ -784,7 +784,7 @@ open Set
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (e : OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) e i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} (e : OrderIso.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) i)) (Fin.val n i)
+  forall {n : Nat} {m : Nat} (e : OrderIso.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_order_iso_apply Fin.coe_orderIso_applyₓ'. -/
 /-- If `e` is an `order_iso` between `fin n` and `fin m`, then `n = m` and `e` is the identity
 map. In this lemma we state that for each `i : fin n` we have `(e i : ℕ) = (i : ℕ)`. -/
@@ -841,7 +841,7 @@ theorem strictMono_unique {f g : Fin n → α} (hf : StrictMono f) (hg : StrictM
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) f)) (Set.range.{u1, 1} α (Fin n) (coeFn.{succ u1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)) (fun (_x : RelEmbedding.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (Fin n) -> α) (RelEmbedding.hasCoeToFun.{0, u1} (Fin n) α (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (Fin.hasLe n) (Preorder.toLE.{u1} α _inst_1)) f g)
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (Function.Embedding.{1, succ u1} (Fin n) α) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => α) _x) (EmbeddingLike.toFunLike.{succ u1, 1, succ u1} (Function.Embedding.{1, succ u1} (Fin n) α) (Fin n) α (Function.instEmbeddingLikeEmbedding.{1, succ u1} (Fin n) α)) (RelEmbedding.toEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) f))) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (Function.Embedding.{1, succ u1} (Fin n) α) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => α) _x) (EmbeddingLike.toFunLike.{succ u1, 1, succ u1} (Function.Embedding.{1, succ u1} (Fin n) α) (Fin n) α (Function.instEmbeddingLikeEmbedding.{1, succ u1} (Fin n) α)) (RelEmbedding.toEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) g)))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) f g)
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)} {g : OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)}, (Eq.{succ u1} (Set.{u1} α) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f)) (Set.range.{u1, 1} α (Fin n) (FunLike.coe.{succ u1, 1, succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => α) _x) (RelHomClass.toFunLike.{u1, 0, u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, u1} (Fin n) α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) g))) -> (Eq.{succ u1} (OrderEmbedding.{0, u1} (Fin n) α (instLEFin n) (Preorder.toLE.{u1} α _inst_1)) f g)
 Case conversion may be inaccurate. Consider using '#align fin.order_embedding_eq Fin.orderEmbedding_eqₓ'. -/
 /-- Two order embeddings of `fin n` are equal provided that their ranges are equal. -/
 theorem orderEmbedding_eq {f g : Fin n ↪o α} (h : range f = range g) : f = g :=
@@ -1276,7 +1276,7 @@ def succEmbedding (n : ℕ) : Fin n ↪o Fin (n + 1) :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succEmbedding n)) (Fin.succ n)
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succEmbedding n))) (Fin.succ n)
+  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succEmbedding n)) (Fin.succ n)
 Case conversion may be inaccurate. Consider using '#align fin.coe_succ_embedding Fin.val_succEmbeddingₓ'. -/
 @[simp]
 theorem val_succEmbedding : ⇑(succEmbedding n) = Fin.succ :=
@@ -1483,7 +1483,7 @@ def castLE (h : n ≤ m) : Fin n ↪o Fin m :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe n m) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE n m h) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n m h)) i)) (Fin.val n i)
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n m h) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast_le Fin.coe_castLEₓ'. -/
 @[simp]
 theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
@@ -1494,7 +1494,7 @@ theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
 lean 3 declaration is
   forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat Nat.hasLt i n) (h : LE.le.{0} Nat Nat.hasLe n m), Eq.{1} (Fin m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) i n m hn h))
 but is expected to have type
-  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat instLTNat i n) (h : LE.le.{0} Nat instLENat n m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) (Fin.mk n i hn)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n m h)) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn h))
+  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat instLTNat i n) (h : LE.le.{0} Nat instLENat n m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin m) (Fin.mk n i hn)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (instLEFin n) (instLEFin m)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_mk Fin.castLE_mkₓ'. -/
 @[simp]
 theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
@@ -1506,7 +1506,7 @@ theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe (Nat.succ n) (Nat.succ m)), Eq.{1} (Fin (Nat.succ m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ m))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) (Fin.castLE (Nat.succ n) (Nat.succ m) h) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (OfNat.mk.{0} (Fin (Nat.succ n)) 0 (Zero.zero.{0} (Fin (Nat.succ n)) (Fin.hasZeroOfNeZero (Nat.succ n) (NeZero.succ n)))))) (OfNat.ofNat.{0} (Fin (Nat.succ m)) 0 (OfNat.mk.{0} (Fin (Nat.succ m)) 0 (Zero.zero.{0} (Fin (Nat.succ m)) (Fin.hasZeroOfNeZero (Nat.succ m) (NeZero.succ m)))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat (Nat.succ n) (Nat.succ m)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m))) (Fin (Nat.succ n)) (Fin (Nat.succ m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE (Nat.succ n) (Nat.succ m) h)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) 0 (Fin.instOfNatFin (Nat.succ m) 0 (NeZero.succ m)))
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat (Nat.succ n) (Nat.succ m)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (instLEFin (Nat.succ n)) (instLEFin (Nat.succ m))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (Nat.succ m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (instLEFin (Nat.succ n)) (instLEFin (Nat.succ m))) (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE (Nat.succ n) (Nat.succ m) h) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) 0 (Fin.instOfNatFin (Nat.succ m) 0 (NeZero.succ m)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_zero Fin.castLE_zeroₓ'. -/
 @[simp]
 theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [eq_iff_veq]
@@ -1516,7 +1516,7 @@ theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by s
 lean 3 declaration is
   forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (Fin.hasLe n) (Fin.hasLe k)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i) n))
 but is expected to have type
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h)))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat instLTNat (Fin.val k i) n))
+  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (instLEFin n) (instLEFin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (instLEFin n) (instLEFin k)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n k h))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat instLTNat (Fin.val k i) n))
 Case conversion may be inaccurate. Consider using '#align fin.range_cast_le Fin.range_castLEₓ'. -/
 @[simp]
 theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i : ℕ) < n } :=
@@ -1527,7 +1527,7 @@ theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i
 lean 3 declaration is
   forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k) (i : Fin k) (hi : Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) => (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k)) (Fin.castLE n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) i hi))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i)
 but is expected to have type
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k) (i : Fin k) (hi : Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) 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(instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n k h)))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n k h)) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin k) _x) (RelHomClass.toFunLike.{0, 0, 0} (RelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE n k h)))) i hi))) (Fin.val k i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
@@ -1541,7 +1541,7 @@ theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi)
 lean 3 declaration is
   forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat Nat.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) (Fin.succ m i)) (Fin.succ n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat Nat.hasLe (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe m n) (Nat.succ_le_succ_iff m n) h)) i))
 but is expected to have type
-  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat instLENat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ m i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h)) (Fin.succ m i)) (Fin.succ n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat instLENat (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat instLENat m n) (Nat.succ_le_succ_iff m n) h))) i))
+  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat instLENat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ m i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) (Fin.succ m i)) (Fin.succ n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat instLENat (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat instLENat m n) (Nat.succ_le_succ_iff m n) h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_succ Fin.castLE_succₓ'. -/
 @[simp]
 theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
@@ -1552,7 +1552,7 @@ theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
 lean 3 declaration is
   forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n) (i : Fin k), Eq.{1} (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n mn) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE k m km) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)) i)
 but is expected to have type
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n) (i : Fin k), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (a : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k m km)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n mn)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k m km)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn))) i)
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n) (i : Fin k), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (a : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin m) a) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k m km) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n mn) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k m km) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_cast_le Fin.castLE_castLEₓ'. -/
 @[simp]
 theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
@@ -1564,7 +1564,7 @@ theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
 lean 3 declaration is
   forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n mn)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE k m km))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)))
 but is expected to have type
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n mn))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k m km)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn))))
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n mn)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin m) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (instLEFin k) (instLEFin m)) (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k m km))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin k) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (instLEFin k) (instLEFin n)) (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_comp_cast_le Fin.castLE_comp_castLEₓ'. -/
 @[simp]
 theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
@@ -1592,7 +1592,7 @@ theorem symm_cast (h : n = m) : (cast h).symm = cast h.symm :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h))) i)) (Fin.val n i)
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast Fin.coe_castₓ'. -/
 /-- While `fin.coe_order_iso_apply` is a more general case of this, we mark this `simp` anyway
 as it is eligible for `dsimp`. -/
@@ -1605,7 +1605,7 @@ theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : ℕ) = i :=
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {h : Eq.{1} Nat n n'}, Eq.{1} (Fin n') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' h) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin n') 0 (OfNat.mk.{0} (Fin n') 0 (Zero.zero.{0} (Fin n') (Fin.hasZeroOfNeZero n' (Eq.mpr.{0} (NeZero.{0} Nat Nat.hasZero n') (NeZero.{0} Nat Nat.hasZero n) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (NeZero.{0} Nat Nat.hasZero n') (NeZero.{0} Nat Nat.hasZero n)) (Eq.ndrec.{0, 1} Nat n' (fun (_a : Nat) => Eq.{1} Prop (NeZero.{0} Nat Nat.hasZero n') (NeZero.{0} Nat Nat.hasZero _a)) (rfl.{1} Prop (NeZero.{0} Nat Nat.hasZero n')) n (Eq.symm.{1} Nat n n' h))) _inst_1)))))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {h : Eq.{1} Nat n n'}, Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n') (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n') _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (Fin n') (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin n'))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n n' h))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ([mdata noImplicitLambda:1 (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n') (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))]) 0 (Fin.instOfNatFin n' 0 (Eq.mpr.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) (id.{0} (Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n)) (Eq.ndrec.{0, 1} Nat n' (fun (_a : Nat) => Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) _a)) (Eq.refl.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n')) n (Eq.symm.{1} Nat n n' h))) (inferInstance.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) _inst_1))))
+  forall {n : Nat} {n' : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {h : Eq.{1} Nat n n'}, Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' h) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ([mdata noImplicitLambda:1 Fin n']) 0 (Fin.instOfNatFin n' 0 (Eq.mpr.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) (id.{0} (Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n)) (Eq.ndrec.{0, 1} Nat n' (fun (_a : Nat) => Eq.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n') (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) _a)) (Eq.refl.{1} Prop (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n')) n (Eq.symm.{1} Nat n n' h))) (inferInstance.{0} (NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.cast_zero Fin.cast_zeroₓ'. -/
 @[simp]
 theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
@@ -1619,7 +1619,7 @@ theorem cast_zero {n' : ℕ} [NeZero n] {h : n = n'} :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) (Fin.last n)) (Fin.last n')
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.last n)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h))) (Fin.last n)) (Fin.last n')
+  forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) (Fin.last n)) (Fin.last n')
 Case conversion may be inaccurate. Consider using '#align fin.cast_last Fin.cast_lastₓ'. -/
 @[simp]
 theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
@@ -1630,7 +1630,7 @@ theorem cast_last {n' : ℕ} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Nat) (hn : LT.lt.{0} Nat Nat.hasLt i n), Eq.{1} (Fin m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) i n m hn (Eq.le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) n m h)))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Nat) (hn : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) (Fin.mk n i hn)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h))) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn (Eq.le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) n m h)))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m) (i : Nat) (hn : LT.lt.{0} Nat instLTNat i n), Eq.{1} (Fin m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn (Eq.le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) n m h)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_mk Fin.cast_mkₓ'. -/
 @[simp]
 theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h.le⟩ :=
@@ -1641,7 +1641,7 @@ theorem cast_mk (h : n = m) (i : ℕ) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i,
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {k : Nat} (h : Eq.{1} Nat n m) (h' : Eq.{1} Nat m k) {i : Fin n}, Eq.{1} (Fin k) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin m) (Fin k) (Fin.hasLe m) (Fin.hasLe k)) (fun (_x : RelIso.{0, 0} (Fin m) (Fin k) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin m) -> (Fin k)) (RelIso.hasCoeToFun.{0, 0} (Fin m) (Fin k) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.cast m k h') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin k) (Fin.hasLe n) (Fin.hasLe k)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.cast n k (Eq.trans.{1} Nat n m k h h')) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} {k : Nat} (h : Eq.{1} Nat n m) (h' : Eq.{1} Nat m k) {i : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin k) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin k)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin k)) (Fin m) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast m k h'))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n k (Eq.trans.{1} Nat n m k h h')))) i)
+  forall {n : Nat} {m : Nat} {k : Nat} (h : Eq.{1} Nat n m) (h' : Eq.{1} Nat m k) {i : Fin n}, Eq.{1} (Fin k) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (fun (_x : Fin m) => Fin k) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin m) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast m k h') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin k) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n k (Eq.trans.{1} Nat n m k h h')) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_trans Fin.cast_transₓ'. -/
 @[simp]
 theorem cast_trans {k : ℕ} (h : n = m) (h' : m = k) {i : Fin n} :
@@ -1662,7 +1662,7 @@ theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) :=
 lean 3 declaration is
   forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat Nat.hasLe m n}, Eq.{1} ((fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (Fin.castLE m n h')) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n h')) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast m n h))
 but is expected to have type
-  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat instLENat m n}, Eq.{1} (forall (a : Fin m), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n h'))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast m n h))))
+  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat instLENat m n}, Eq.{1} (forall (a : Fin m), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin n) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (instLEFin m) (instLEFin n)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castLE m n h')) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (fun (_x : Fin m) => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast m n h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_le_of_eq Fin.castLE_of_eqₓ'. -/
 theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
     (castLE h' : Fin m → Fin n) = Fin.cast h :=
@@ -1683,7 +1683,7 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (Fin.cast n m h)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h)) (cast.{1} (Fin n) (Fin m) (Eq.subst.{1} Nat (fun (_x : Nat) => Eq.{2} Type (Fin n) (Fin _x)) n m h (rfl.{2} Type (Fin n))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8323 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8324 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8323) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8323) (rfl.{1} Nat n) m h)))))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((Fin n) -> (Fin m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m h)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8776 : Fin n) => Fin m) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8319 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8320 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8319) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8319) (rfl.{1} Nat n) m h)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
@@ -1705,7 +1705,7 @@ def castAdd (m) : Fin n ↪o Fin (n + m) :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) i)) (Fin.val n i)
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast_add Fin.coe_castAddₓ'. -/
 @[simp]
 theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
@@ -1716,7 +1716,7 @@ theorem coe_castAdd (m : ℕ) (i : Fin n) : (castAdd m i : ℕ) = i :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} ((fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n) (Fin.hasLe n) (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n) -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n n (rfl.{1} Nat n)))
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n)) (Fin n) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n n (rfl.{1} Nat n)))))
+  forall {n : Nat}, Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n (rfl.{1} Nat n)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_zero Fin.castAdd_zeroₓ'. -/
 @[simp]
 theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = cast rfl :=
@@ -1727,7 +1727,7 @@ theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = cast rfl :=
 lean 3 declaration is
   forall {m : Nat} (n : Nat) (i : Fin m), LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) m
 but is expected to have type
-  forall {m : Nat} (n : Nat) (i : Fin m), LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd m n)) i)) m
+  forall {m : Nat} (n : Nat) (i : Fin m), LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) m
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_lt Fin.castAdd_ltₓ'. -/
 theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAdd n i : ℕ) < m :=
   i.2
@@ -1737,7 +1737,7 @@ theorem castAdd_lt {m : ℕ} (n : ℕ) (i : Fin m) : (castAdd n i : ℕ) < m :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Nat) (h : LT.lt.{0} Nat Nat.hasLt i n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i (Nat.lt_add_right i n m h))
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i (Nat.lt_add_right i n m h))
+  forall {n : Nat} (m : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i (Nat.lt_add_right i n m h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_mk Fin.castAdd_mkₓ'. -/
 @[simp]
 theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i, lt_add_right i n m h⟩ :=
@@ -1748,7 +1748,7 @@ theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (hi : LT.lt.{0} Nat Nat.hasLt (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i hi)) i
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (hi : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i) n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) i
+  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (hi : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i) n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast_lt Fin.castAdd_castLTₓ'. -/
 @[simp]
 theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m (castLT i hi) = i :=
@@ -1759,7 +1759,7 @@ theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i) (Fin.castAdd_lt n m i)) i
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) i) (Fin.castAdd_lt n m i)) i
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) i) (Fin.castAdd_lt n m i)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_add Fin.castLT_castAddₓ'. -/
 @[simp]
 theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt m i) = i :=
@@ -1770,7 +1770,7 @@ theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n')) (fun (_x : Fin ((fun 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x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8623 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8623 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (n' : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n' m) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -1782,7 +1782,7 @@ theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n (add_right_cancel.{0} Nat Nat.hasAdd (AddRightCancelSemigroup.toIsRightCancelAdd.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) n' m n h)) i))
 but is expected to have type
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n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n' m) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n (add_right_cancel.{0} Nat instAddNat (IsCancelAdd.toIsRightCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n' m n h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_add_left Fin.cast_castAdd_leftₓ'. -/
 theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (castAdd m i) = castAdd m (cast (add_right_cancel h) i) :=
@@ -1793,7 +1793,7 @@ theorem cast_castAdd_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m')))) (Fin.castAdd n m') i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m')) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) h))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m')) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) i)
+  forall {n : Nat} {m : Nat} {m' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m') i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd n m) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_add_right Fin.cast_castAdd_rightₓ'. -/
 @[simp]
 theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
@@ -1805,7 +1805,7 @@ theorem cast_castAdd_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
 lean 3 declaration is
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 but is expected to have type
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0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) n p)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) m n) p) (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) m n) p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat Nat.addSemigroup)) n p)) (add_assoc.{0} Nat Nat.addSemigroup m n p))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p)))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p)))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n p)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast_add Fin.castAdd_castAddₓ'. -/
 theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
     castAdd p (castAdd n i) = cast (add_assoc _ _ _).symm (castAdd (n + p) i) :=
@@ -1816,7 +1816,7 @@ theorem castAdd_castAdd {m n p : ℕ} (i : Fin m) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (Nat.succ n) (Nat.succ n')), Eq.{1} (Fin (Nat.succ n')) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ n'))) (fun (_x : RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ n'))) (RelIso.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) (Fin.cast (Nat.succ n) (Nat.succ n') h) (Fin.succ n i)) (Fin.succ n' (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' (Nat.succ.inj n n' h)) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (Nat.succ n) (Nat.succ n')), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ n')) (Fin.succ n i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ n'))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ n')) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ n'))) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ n')))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (Nat.succ n) (Nat.succ n') h))) (Fin.succ n i)) (Fin.succ n' (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n') _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (Fin n') (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin n'))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n n' (Nat.succ.inj n n' h)))) i))
+  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (Nat.succ n) (Nat.succ n')), Eq.{1} (Fin (Nat.succ n')) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => Fin (Nat.succ n')) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (Nat.succ n) (Nat.succ n') h) (Fin.succ n i)) (Fin.succ n' (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' (Nat.succ.inj n n' h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_eq Fin.cast_succ_eqₓ'. -/
 /-- The cast of the successor is the succesor of the cast. See `fin.succ_cast_eq` for rewriting in
 the reverse direction. -/
@@ -1830,7 +1830,7 @@ theorem cast_succ_eq {n' : ℕ} (i : Fin n) (h : n.succ = n'.succ) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat n n'), Eq.{1} (Fin (Nat.succ n')) (Fin.succ n' (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ n'))) (fun (_x : RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ n'))) (RelIso.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ n')) (Fin.hasLe (Nat.succ n')))) (Fin.cast (Nat.succ n) (Nat.succ n') (Eq.mpr.{0} (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n')) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n'))) (Eq.ndrec.{0, 1} Nat n (fun (_a : Nat) => Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ _a) (Nat.succ n'))) (rfl.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n'))) n' h)) (rfl.{1} Nat (Nat.succ n')))) (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat n n'), Eq.{1} (Fin (Nat.succ n')) (Fin.succ n' (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n') _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (Fin n') (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin n'))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n n' h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ n'))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ n')) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ n'))) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ n')))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (Nat.succ n) (Nat.succ n') (Eq.mpr.{0} (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n')) (id.{0} (Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n'))) (Eq.ndrec.{0, 1} Nat n (fun (_a : Nat) => Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ _a) (Nat.succ n'))) (Eq.refl.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n'))) n' h)) (Eq.refl.{1} Nat (Nat.succ n')))))) (Fin.succ n i))
+  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat n n'), Eq.{1} (Fin (Nat.succ n')) (Fin.succ n' (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' h) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => Fin (Nat.succ n')) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (Nat.succ n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (Nat.succ n')) => LE.le.{0} (Fin (Nat.succ n')) (instLEFin (Nat.succ n')) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (Nat.succ n) (Nat.succ n') (Eq.mpr.{0} (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n')) (id.{0} (Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ n') (Nat.succ n'))) (Eq.ndrec.{0, 1} Nat n (fun (_a : Nat) => Eq.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n')) (Eq.{1} Nat (Nat.succ _a) (Nat.succ n'))) (Eq.refl.{1} Prop (Eq.{1} Nat (Nat.succ n) (Nat.succ n'))) n' h)) (Eq.refl.{1} Nat (Nat.succ n')))) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_cast_eq Fin.succ_cast_eqₓ'. -/
 theorem succ_cast_eq {n' : ℕ} (i : Fin n) (h : n = n') :
     (cast h i).succ = cast (by rw [h]) i.succ :=
@@ -1848,7 +1848,7 @@ def castSucc : Fin n ↪o Fin (n + 1) :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (Fin.val n i)
+  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (Fin.val n i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_cast_succ Fin.coe_castSuccₓ'. -/
 @[simp]
 theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
@@ -1859,7 +1859,7 @@ theorem coe_castSucc (i : Fin n) : (i.cast_succ : ℕ) = i :=
 lean 3 declaration is
   forall (n : Nat) (i : Nat) (h : LT.lt.{0} Nat Nat.hasLt i n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i (Nat.lt.step i n h))
 but is expected to have type
-  forall (n : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i (Nat.lt.step i n h))
+  forall (n : Nat) (i : Nat) (h : LT.lt.{0} Nat instLTNat i n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.mk n i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) (Fin.mk n i h)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i (Nat.lt.step i n h))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_mk Fin.castSucc_mkₓ'. -/
 @[simp]
 theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ :=
@@ -1870,7 +1870,7 @@ theorem castSucc_mk (n i : ℕ) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {i : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' 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n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n n' (Nat.succ_injective n n' h)))) i))
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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' (Nat.succ_injective n n' h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_cast_succ Fin.cast_castSuccₓ'. -/
 @[simp]
 theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
@@ -1884,7 +1884,7 @@ theorem cast_castSucc {n' : ℕ} {h : n + 1 = n' + 1} {i : Fin n} :
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) (Fin.succ n i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i) (Fin.succ n i)
+  forall {n : Nat} (i : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_succ Fin.castSucc_lt_succₓ'. -/
 theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
   lt_iff_val_lt_val.2 <| by simp only [coe_cast_succ, coe_succ, Nat.lt_succ_self]
@@ -1894,7 +1894,7 @@ theorem castSucc_lt_succ (i : Fin n) : i.cast_succ < i.succ :=
 lean 3 declaration is
   forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {j : Fin n}, Iff (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) j)) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i (Fin.succ n j))
 but is expected to have type
-  forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin n}, Iff (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) j)) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (Fin.succ n j))
+  forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {j : Fin n}, Iff (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) j)) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i (Fin.succ n j))
 Case conversion may be inaccurate. Consider using '#align fin.le_cast_succ_iff Fin.le_castSucc_iffₓ'. -/
 theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i < j.succ := by
   simpa [lt_iff_coe_lt_coe, le_iff_coe_le_coe] using nat.succ_le_succ_iff.symm
@@ -1904,7 +1904,7 @@ theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.cast_succ ↔ i
 lean 3 declaration is
   forall {n : Nat} {i : Fin n} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) j) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n)) (Fin.succ n i) j)
 but is expected to have type
-  forall {n : Nat} {i : Fin n} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i) j) (LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) (Fin.succ n i) j)
+  forall {n : Nat} {i : Fin n} {j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) j) (LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) (Fin.succ n i) j)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_iff_succ_le Fin.castSucc_lt_iff_succ_leₓ'. -/
 theorem castSucc_lt_iff_succ_le {n : ℕ} {i : Fin n} {j : Fin (n + 1)} :
     i.cast_succ < j ↔ i.succ ≤ j := by
@@ -1930,7 +1930,7 @@ theorem succ_eq_last_succ {n : ℕ} (i : Fin n.succ) : i.succ = last (n + 1) ↔
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i h)) i
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) i
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_lt Fin.castSucc_castLTₓ'. -/
 @[simp]
 theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT i h) = i :=
@@ -1941,7 +1941,7 @@ theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT
 lean 3 declaration is
   forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) h) a
 but is expected to have type
-  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat instLTNat (Fin.val n a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) h) a
+  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat instLTNat (Fin.val n a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) h) a
 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_succ Fin.castLT_castSuccₓ'. -/
 @[simp]
 theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSucc a) h = a := by
@@ -1952,7 +1952,7 @@ theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (cast
 lean 3 declaration is
   forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) b)) (LT.lt.{0} (Fin n) (Fin.hasLt n) a b)
 but is expected to have type
-  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) b)) (LT.lt.{0} (Fin n) (instLTFin n) a b)
+  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) b)) (LT.lt.{0} (Fin n) (instLTFin n) a b)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_cast_succ_iff Fin.castSucc_lt_castSucc_iffₓ'. -/
 @[simp]
 theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
@@ -1963,7 +1963,7 @@ theorem castSucc_lt_castSucc_iff : a.cast_succ < b.cast_succ ↔ a < b :=
 lean 3 declaration is
   forall (n : Nat), Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n))
 but is expected to have type
-  forall (n : Nat), Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)))
+  forall (n : Nat), Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_injective Fin.castSucc_injectiveₓ'. -/
 theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
   (castSucc : Fin n ↪o _).Injective
@@ -1973,7 +1973,7 @@ theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) b)) (Eq.{1} (Fin n) a b)
 but is expected to have type
-  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) b)) (Eq.{1} (Fin n) a b)
+  forall {n : Nat} {a : Fin n} {b : Fin n}, Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) b)) (Eq.{1} (Fin n) a b)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_inj Fin.castSucc_injₓ'. -/
 theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
   (castSucc_injective n).eq_iff
@@ -1983,7 +1983,7 @@ theorem castSucc_inj {a b : Fin n} : a.cast_succ = b.cast_succ ↔ a = b :=
 lean 3 declaration is
   forall {n : Nat} (a : Fin n), LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (Fin.last n)
 but is expected to have type
-  forall {n : Nat} (a : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) (Fin.last n)
+  forall {n : Nat} (a : Fin n), LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (Fin.last n)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_lt_last Fin.castSucc_lt_lastₓ'. -/
 theorem castSucc_lt_last (a : Fin n) : castSucc a < last n :=
   lt_iff_val_lt_val.mpr a.is_lt
@@ -1993,7 +1993,7 @@ theorem castSucc_lt_last (a : Fin n) : castSucc a < last n :=
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n], Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n], Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n], Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_zero Fin.castSucc_zeroₓ'. -/
 @[simp]
 theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
@@ -2004,7 +2004,7 @@ theorem castSucc_zero [NeZero n] : castSucc (0 : Fin n) = 0 :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} Nat Nat.hasOne)) (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_one Fin.castSucc_oneₓ'. -/
 @[simp]
 theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
@@ -2015,7 +2015,7 @@ theorem castSucc_one {n : ℕ} : Fin.castSucc (1 : Fin (n + 2)) = 1 :=
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {i : Fin n}, (LT.lt.{0} (Fin n) (Fin.hasLt n) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))) i) -> (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {i : Fin n}, (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {i : Fin n}, (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_pos Fin.castSucc_posₓ'. -/
 /-- `cast_succ i` is positive when `i` is positive -/
 theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
@@ -2026,7 +2026,7 @@ theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (a : Fin n), Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Eq.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_eq_zero_iff Fin.castSucc_eq_zero_iffₓ'. -/
 @[simp]
 theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0 :=
@@ -2037,7 +2037,7 @@ theorem castSucc_eq_zero_iff [NeZero n] (a : Fin n) : a.cast_succ = 0 ↔ a = 0
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (a : Fin n), Iff (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Ne.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Ne.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Ne.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (a : Fin n), Iff (Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Ne.{1} (Fin n) a (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iffₓ'. -/
 theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a ≠ 0 :=
   not_iff_not.mpr <| castSucc_eq_zero_iff a
@@ -2047,7 +2047,7 @@ theorem castSucc_ne_zero_iff [NeZero n] (a : Fin n) : a.cast_succ ≠ 0 ↔ a 
 lean 3 declaration is
   forall (n : Nat) (j : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (Nat.succ n)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (Nat.succ n)) (Fin.succ n j)) (Fin.succ (Nat.succ n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) j))
 but is expected to have type
-  forall (n : Nat) (j : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ n j)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc (Nat.succ n))) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) j))
+  forall (n : Nat) (j : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ n j)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (Nat.succ n)) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) j))
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_fin_succ Fin.castSucc_fin_succₓ'. -/
 theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.succ (castSucc j) := by
   simp [Fin.ext_iff]
@@ -2057,7 +2057,7 @@ theorem castSucc_fin_succ (n : ℕ) (j : Fin n) : castSucc (Fin.succ j) = Fin.su
 lean 3 declaration is
   forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HasLiftT.mk.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (CoeTCₓ.coe.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeTrans.{1, 1, 1} (Fin n) Nat (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Nat.castCoe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.addMonoidWithOne (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (NeZero.succ n)))) (Fin.coeToNat n)))) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a)
 but is expected to have type
-  forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) (Fin.val n a)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a)
+  forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) (Fin.val n a)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a)
 Case conversion may be inaccurate. Consider using '#align fin.coe_eq_cast_succ Fin.coe_eq_castSuccₓ'. -/
 @[norm_cast, simp]
 theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
@@ -2070,7 +2070,7 @@ theorem coe_eq_castSucc : (a : Fin (n + 1)) = a.cast_succ :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HAdd.hAdd.{0, 0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (instHAdd.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasAdd (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.succ n a)
 but is expected to have type
-  forall {n : Nat} {a : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instHAdd.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (Fin.instAddFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 1 (NeZero.succ n)))) (Fin.succ n a)
+  forall {n : Nat} {a : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instHAdd.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (Fin.instAddFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) 1 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 1 (NeZero.succ n)))) (Fin.succ n a)
 Case conversion may be inaccurate. Consider using '#align fin.coe_succ_eq_succ Fin.coeSucc_eq_succₓ'. -/
 @[simp]
 theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
@@ -2084,7 +2084,7 @@ theorem coeSucc_eq_succ : a.cast_succ + 1 = a.succ :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n}, LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) (Fin.succ n a)
 but is expected to have type
-  forall {n : Nat} {a : Fin n}, LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) (Fin.succ n a)
+  forall {n : Nat} {a : Fin n}, LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) a) (Fin.succ n a)
 Case conversion may be inaccurate. Consider using '#align fin.lt_succ Fin.lt_succₓ'. -/
 theorem lt_succ : a.cast_succ < a.succ :=
   by
@@ -2096,7 +2096,7 @@ theorem lt_succ : a.cast_succ < a.succ :=
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n))) (setOf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) i) n))
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)))) (setOf.{0} (Fin (Nat.succ n)) (fun (i : Fin (Nat.succ n)) => LT.lt.{0} Nat instLTNat (Fin.val (Nat.succ n) i) n))
+  forall {n : Nat}, Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n))) (setOf.{0} (Fin (Nat.succ n)) (fun (i : Fin (Nat.succ n)) => LT.lt.{0} Nat instLTNat (Fin.val (Nat.succ n) i) n))
 Case conversion may be inaccurate. Consider using '#align fin.range_cast_succ Fin.range_castSuccₓ'. -/
 @[simp]
 theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = { i | (i : ℕ) < n } :=
@@ -2107,7 +2107,7 @@ theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) =
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (hi : Membership.Mem.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.hasMem.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) i (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n)))), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) Type (Set.hasCoeToSort.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n)))) i hi))) (Fin.val (Nat.succ n) i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
@@ -2121,7 +2121,7 @@ theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (Nat.succ n)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc (Nat.succ n))) (Fin.succ n i))
+  forall {n : Nat} (i : Fin n), Eq.{1} (Fin (Nat.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ n)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_cast_succ Fin.succ_castSuccₓ'. -/
 theorem succ_castSucc {n : ℕ} (i : Fin n) : i.cast_succ.succ = i.succ.cast_succ :=
   Fin.ext (by simp)
@@ -2139,7 +2139,7 @@ def addNat (m) : Fin n ↪o Fin (n + m) :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i) m)
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) m)
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) m)
 Case conversion may be inaccurate. Consider using '#align fin.coe_add_nat Fin.coe_addNatₓ'. -/
 @[simp]
 theorem coe_addNat (m : ℕ) (i : Fin n) : (addNat m i : ℕ) = i + m :=
@@ -2150,7 +2150,7 @@ theorem coe_addNat (m : ℕ) (i : Fin n) : (addNat m i : ℕ) = i + m :=
 lean 3 declaration is
   forall {n : Nat} {i : Fin n}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.addNat n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i) (Fin.succ n i)
 but is expected to have type
-  forall {n : Nat} {i : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (Fin.succ n i)
+  forall {n : Nat} {i : Fin n}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_one Fin.addNat_oneₓ'. -/
 @[simp]
 theorem addNat_one {i : Fin n} : addNat 1 i = i.succ :=
@@ -2163,7 +2163,7 @@ theorem addNat_one {i : Fin n} : addNat 1 i = i.succ :=
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i))
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) i))
+  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i))
 Case conversion may be inaccurate. Consider using '#align fin.le_coe_add_nat Fin.le_coe_addNatₓ'. -/
 theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNat m i :=
   Nat.le_add_left _ _
@@ -2173,7 +2173,7 @@ theorem le_coe_addNat (m : ℕ) (i : Fin n) : m ≤ addNat m i :=
 lean 3 declaration is
   forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat Nat.hasLt i m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.addNat m n) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n) (add_lt_add_right.{0} Nat Nat.hasAdd Nat.hasLt (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 but is expected to have type
-  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat m n)) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n) (add_lt_add_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
+  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat m n) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n) (add_lt_add_right.{0} Nat instAddNat instLTNat (AddRightCancelSemigroup.covariant_swap_add_lt_of_covariant_swap_add_le.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_right.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_mk Fin.addNat_mkₓ'. -/
 @[simp]
 theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, add_lt_add_right hi n⟩ :=
@@ -2184,7 +2184,7 @@ theorem addNat_mk (n i : ℕ) (hi : i < m) : addNat n ⟨i, hi⟩ = ⟨i + n, ad
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) n'), Eq.{1} (Fin n') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin n') (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin n') (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) n' h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) (Fin.addNat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))))) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))))) n (add_zero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) n'), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => Fin n') (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => Fin n') _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n'))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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(OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n') _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (Fin n') (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin n'))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n (add_zero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)))) i)
+  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) n'), Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) n' h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) n (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n (add_zero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_zero Fin.cast_addNat_zeroₓ'. -/
 @[simp]
 theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
@@ -2196,7 +2196,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n' m) i))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2208,7 +2208,7 @@ theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n (add_right_cancel.{0} Nat Nat.hasAdd (AddRightCancelSemigroup.toIsRightCancelAdd.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) n' m n h)) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) h))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n (add_right_cancel.{0} Nat instAddNat (IsCancelAdd.toIsRightCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n' m n h)))) i))
+  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n (add_right_cancel.{0} Nat instAddNat (IsCancelAdd.toIsRightCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) n' m n h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_left Fin.cast_addNat_leftₓ'. -/
 theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
     cast h (addNat m i) = addNat m (cast (add_right_cancel h) i) :=
@@ -2219,7 +2219,7 @@ theorem cast_addNat_left {n n' m : ℕ} (i : Fin n') (h : n' + m = n + m) :
 lean 3 declaration is
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 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m'))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m') i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_right Fin.cast_addNat_rightₓ'. -/
 @[simp]
 theorem cast_addNat_right {n m m' : ℕ} (i : Fin n) (h : n + m' = n + m) :
@@ -2239,7 +2239,7 @@ def natAdd (n) {m} : Fin m ↪o Fin (n + m) :=
 lean 3 declaration is
   forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) i))
 but is expected to have type
-  forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd n m)) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (Fin.val m i))
+  forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} Nat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd n m) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (Fin.val m i))
 Case conversion may be inaccurate. Consider using '#align fin.coe_nat_add Fin.coe_natAddₓ'. -/
 @[simp]
 theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAdd n i : ℕ) = n + i :=
@@ -2250,7 +2250,7 @@ theorem coe_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : (natAdd n i : ℕ) = n + i
 lean 3 declaration is
   forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat Nat.hasLt i m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n i) (add_lt_add_left.{0} Nat Nat.hasAdd Nat.hasLt (AddLeftCancelSemigroup.covariant_add_lt_of_covariant_add_le.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 but is expected to have type
-  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd n m)) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n i) (add_lt_add_left.{0} Nat instAddNat instLTNat (AddLeftCancelSemigroup.covariant_add_lt_of_covariant_add_le.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
+  forall {m : Nat} (n : Nat) (i : Nat) (hi : LT.lt.{0} Nat instLTNat i m), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.mk m i hi)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd n m) (Fin.mk m i hi)) (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n i) (add_lt_add_left.{0} Nat instAddNat instLTNat (AddLeftCancelSemigroup.covariant_add_lt_of_covariant_add_le.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))) i m hi n))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_mk Fin.natAdd_mkₓ'. -/
 @[simp]
 theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAdd n ⟨i, hi⟩ = ⟨n + i, add_lt_add_left hi n⟩ :=
@@ -2261,7 +2261,7 @@ theorem natAdd_mk (n i : ℕ) (hi : i < m) : natAdd n ⟨i, hi⟩ = ⟨n + i, ad
 lean 3 declaration is
   forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i))
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) i))
+  forall {n : Nat} (m : Nat) (i : Fin n), LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i))
 Case conversion may be inaccurate. Consider using '#align fin.le_coe_nat_add Fin.le_coe_natAddₓ'. -/
 theorem le_coe_natAdd (m : ℕ) (i : Fin n) : m ≤ natAdd m i :=
   Nat.le_add_right _ _
@@ -2283,7 +2283,7 @@ theorem natAdd_zero {n : ℕ} : Fin.natAdd 0 = (Fin.cast (zero_add n).symm).toRe
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) (Fin.natAdd m n') i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) (congr_arg.{1, 1} Nat Nat n' n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n')) i))
+  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (a._@.Mathlib.Order.RelIso.Basic._hyg.8776 : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') 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 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast Fin.natAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_nat_add_right`. -/
 theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2295,7 +2295,7 @@ theorem natAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n) h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n'))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n')))) (Fin.natAdd m n') i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n (add_left_cancel.{0} Nat Nat.hasAdd (AddLeftCancelSemigroup.toIsLeftCancelAdd.{0} Nat (AddLeftCancelMonoid.toAddLeftCancelSemigroup.{0} Nat (AddCancelCommMonoid.toAddLeftCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n' n h)) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n')) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) h))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n')) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n (add_left_cancel.{0} Nat instAddNat (IsCancelAdd.toIsLeftCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n' n h)))) i))
+  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n') (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin n') (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n'))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n')) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n') i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (fun (_x : Fin n') => Fin n) (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n' n (add_left_cancel.{0} Nat instAddNat (IsCancelAdd.toIsLeftCancelAdd.{0} Nat instAddNat (AddCancelMonoid.toIsCancelAdd.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n' n h)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_right Fin.cast_natAdd_rightₓ'. -/
 theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
     cast h (natAdd m i) = natAdd m (cast (add_left_cancel h) i) :=
@@ -2306,7 +2306,7 @@ theorem cast_natAdd_right {n n' m : ℕ} (i : Fin n') (h : m + n' = m + n) :
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_left Fin.cast_natAdd_leftₓ'. -/
 @[simp]
 theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
@@ -2318,7 +2318,7 @@ theorem cast_natAdd_left {n m m' : ℕ} (i : Fin n) (h : m' + n = m + n) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat_add Fin.castAdd_natAddₓ'. -/
 theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     castAdd p (natAdd m i) = cast (add_assoc _ _ _).symm (natAdd m (castAdd p i)) :=
@@ -2329,7 +2329,7 @@ theorem castAdd_natAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
 lean 3 declaration is
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 but is expected to have type
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instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast_add Fin.natAdd_castAddₓ'. -/
 theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
     natAdd m (castAdd p i) = cast (add_assoc _ _ _) (castAdd p (natAdd m i)) :=
@@ -2340,7 +2340,7 @@ theorem natAdd_castAdd (p m : ℕ) {n : ℕ} (i : Fin n) :
 lean 3 declaration is
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 but is expected to have type
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instAddNat) m n) p)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin p) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) (instLEFin p) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p))) (Fin p) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin p) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin p) => LE.le.{0} (Fin p) (instLEFin p) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin p) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin p) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin p) => LE.le.{0} (Fin p) (instLEFin p) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n) p) i))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_nat_add Fin.natAdd_natAddₓ'. -/
 theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
     natAdd m (natAdd n i) = cast (add_assoc _ _ _) (natAdd (m + n) i) :=
@@ -2351,7 +2351,7 @@ theorem natAdd_natAdd (m n : ℕ) {p : ℕ} (i : Fin p) :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) n'), Eq.{1} (Fin n') (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin n') (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin n') (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) n' h) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin n') (Fin.hasLe n) (Fin.hasLe n')) (fun (_x : RelIso.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) => (Fin n) -> (Fin n')) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin n') (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin n') (Fin.hasLe n'))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toHasAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat (AddZeroClass.toHasZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
 but is expected to have type
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(instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n')) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => Fin n') _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) 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(instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) n' h))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin n') _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin n')) (Fin n) (Fin n') (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin n'))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)))) i)
+  forall {n : Nat} {n' : Nat} (i : Fin n) (h : Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) n'), Eq.{1} (Fin n') (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) n' h) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) i)) (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (fun (_x : Fin n) => Fin n') (RelHomClass.toFunLike.{0, 0, 0} (RelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{0, 0} (Fin n) (Fin n') (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Fin.cast n n' (Eq.trans.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n' (Eq.symm.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid))) (OfNat.ofNat.{0} Nat 0 (Zero.toOfNat0.{0} Nat (AddZeroClass.toZero.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) n) n (zero_add.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) n)) h)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add_zero Fin.cast_natAdd_zeroₓ'. -/
 @[simp]
 theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
@@ -2363,7 +2363,7 @@ theorem cast_natAdd_zero {n n' : ℕ} (i : Fin n) (h : 0 + n = n') :
 lean 3 declaration is
   forall (n : Nat) {m : Nat} (i : Fin m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat 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 but is expected to have type
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(AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun 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Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : 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(instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat m n) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_nat_add Fin.cast_natAddₓ'. -/
 @[simp]
 theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAdd n i) = addNat n i :=
@@ -2374,7 +2374,7 @@ theorem cast_natAdd (n : ℕ) {m : ℕ} (i : Fin m) : cast (add_comm _ _) (natAd
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.cast_add_nat Fin.cast_addNatₓ'. -/
 @[simp]
 theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNat m i) = natAdd m i :=
@@ -2385,7 +2385,7 @@ theorem cast_addNat {n : ℕ} (m : ℕ) (i : Fin n) : cast (add_comm _ _) (addNa
 lean 3 declaration is
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 but is expected to have type
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+  forall {m : Nat} {n : Nat}, Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.last m)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m 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1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m 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(instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.last m)) (Fin.last (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_last Fin.natAdd_lastₓ'. -/
 @[simp]
 theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
@@ -2396,7 +2396,7 @@ theorem natAdd_last {m n : ℕ} : natAdd n (last m) = last (n + m) :=
 lean 3 declaration is
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x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd n m) i))
 Case conversion may be inaccurate. Consider using '#align fin.nat_add_cast_succ Fin.natAdd_castSuccₓ'. -/
 theorem natAdd_castSucc {m n : ℕ} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
   rfl
@@ -2553,7 +2553,7 @@ theorem subNat_mk {i : ℕ} (h₁ : i < n + m) (h₂ : m ≤ i) :
 lean 3 declaration is
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(Nat.succ n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (Nat.succ n)) (Fin.succ n i)) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Fin.castSucc_pos (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n) (Fin.succ n i) (Fin.succ_pos n i)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)
 Case conversion may be inaccurate. Consider using '#align fin.pred_cast_succ_succ Fin.pred_castSucc_succₓ'. -/
 @[simp]
 theorem pred_castSucc_succ (i : Fin n) :
@@ -2565,7 +2565,7 @@ theorem pred_castSucc_succ (i : Fin n) :
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)} (h : LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) i)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (Fin.subNat n m i h)) i
 but is expected to have type
-  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat n m i h)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (Fin.subNat n m i h)) i
+  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat n m i h)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) (Fin.subNat n m i h)) i
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_sub_nat Fin.addNat_subNatₓ'. -/
 @[simp]
 theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat m (subNat m i h) = i :=
@@ -2576,7 +2576,7 @@ theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat m (subNat m i h)
 lean 3 declaration is
   forall {n : Nat} (i : Fin n) (m : Nat) (h : optParam.{0} (LE.le.{0} Nat Nat.hasLe m ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i))) (Fin.le_coe_addNat n m i)), Eq.{1} (Fin n) (Fin.subNat n m (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) i) h) i
 but is expected to have type
-  forall {n : Nat} (i : Fin n) (m : Nat) (h : optParam.{0} (LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) i))) (Fin.le_coe_addNat n m i)), Eq.{1} (Fin n) (Fin.subNat n m (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) i) h) i
+  forall {n : Nat} (i : Fin n) (m : Nat) (h : optParam.{0} (LE.le.{0} Nat instLENat m (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i))) (Fin.le_coe_addNat n m i)), Eq.{1} (Fin n) (Fin.subNat n m (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.addNat n m) i) h) i
 Case conversion may be inaccurate. Consider using '#align fin.sub_nat_add_nat Fin.subNat_addNatₓ'. -/
 @[simp]
 theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addNat m i) :
@@ -2588,7 +2588,7 @@ theorem subNat_addNat (i : Fin n) (m : ℕ) (h : m ≤ addNat m i := le_coe_addN
 lean 3 declaration is
   forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)} (h : LE.le.{0} Nat Nat.hasLe n ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))))) i)), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.natAdd n m) (Fin.subNat m n (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n) (add_comm.{0} Nat Nat.addCommSemigroup n m)) i) h)) i
 but is expected to have type
-  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat n (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat m n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat 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Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n) (add_comm.{0} Nat Nat.addCommSemigroup n m)))) i) h)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd n m)) (Fin.subNat m n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n) (add_comm.{0} Nat Nat.addCommSemigroup n m)))) i) h)) i
+  forall {n : Nat} {m : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)} (h : LE.le.{0} Nat instLENat n (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i)), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.subNat m n (FunLike.coe.{1, 1, 1} (RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddCommSemigroup.toAddSemigroup.{0} Nat Nat.addCommSemigroup))) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat 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 Case conversion may be inaccurate. Consider using '#align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castₓ'. -/
 @[simp]
 theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
@@ -2699,7 +2699,7 @@ theorem succRecOn_succ {C : ∀ n, Fin n → Sort _} {H0 Hs} {n} (i : Fin n) :
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), C i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
 Case conversion may be inaccurate. Consider using '#align fin.induction Fin.inductionₓ'. -/
 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
@@ -2719,7 +2719,7 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.induction.{u1} n C h0 hs (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13330 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13330) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13326 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13326) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
 Case conversion may be inaccurate. Consider using '#align fin.induction_zero Fin.induction_zeroₓ'. -/
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2731,7 +2731,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) (Fin.induction.{u1} n C h0 hs (Fin.succ n i)) (hs i (Fin.induction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13522 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13522) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13518 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13518) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2743,7 +2743,7 @@ theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (C i)
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) -> (C i)
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) -> (C i)
 Case conversion may be inaccurate. Consider using '#align fin.induction_on Fin.inductionOnₓ'. -/
 /-- Define `C i` by induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
 This function has two arguments: `h0` handles the base case on `C 0`,
@@ -2881,7 +2881,7 @@ theorem fin_two_eq_of_eq_zero_iff {a b : Fin 2} (h : a = 0 ↔ b = 0) : a = b :=
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), (C (Fin.succ n i)) -> (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), C i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
 Case conversion may be inaccurate. Consider using '#align fin.reverse_induction Fin.reverseInductionₓ'. -/
 /--
 Define `C i` by reverse induction on `i : fin (n + 1)` via induction on the underlying `nat` value.
@@ -2907,7 +2907,7 @@ def reverseInduction {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))), Eq.{u1} ((fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) (Fin.last n)) (Fin.reverseInduction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (Fin.last n)) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i))), Eq.{u1} (C (Fin.last n)) (Fin.reverseInduction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) h0 hs (Fin.last n)) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))), Eq.{u1} (C (Fin.last n)) (Fin.reverseInduction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) h0 hs (Fin.last n)) h0
 Case conversion may be inaccurate. Consider using '#align fin.reverse_induction_last Fin.reverse_induction_lastₓ'. -/
 @[simp]
 theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
@@ -2920,7 +2920,7 @@ theorem reverse_induction_last {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (F
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))) (i : Fin n), Eq.{u1} ((fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (Fin.reverseInduction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (hs i (Fin.reverseInduction.{u1} n (fun (_x : Fin (Nat.succ n)) => C _x) h0 hs (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i))) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (Fin.reverseInduction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (hs i (Fin.reverseInduction.{u1} n (fun (_x : Fin (Nat.succ n)) => C _x) h0 hs (Fin.succ n i)))
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (Fin.last n)) (hs : forall (i : Fin n), (C (Fin.succ n i)) -> (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (Fin.reverseInduction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (hs i (Fin.reverseInduction.{u1} n (fun (_x : Fin (Nat.succ n)) => C _x) h0 hs (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.reverse_induction_cast_succ Fin.reverse_induction_castSuccₓ'. -/
 @[simp]
 theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 : C (Fin.last n))
@@ -2936,7 +2936,7 @@ theorem reverse_induction_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (h0 :
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), C i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}}, (C (Fin.last n)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), C i)
 Case conversion may be inaccurate. Consider using '#align fin.last_cases Fin.lastCasesₓ'. -/
 /-- Define `f : Π i : fin n.succ, C i` by separately handling the cases `i = fin.last n` and
 `i = j.cast_succ`, `j : fin n`. -/
@@ -2950,7 +2950,7 @@ def lastCases {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)), Eq.{u1} ((fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) (Fin.last n)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) hlast hcast (Fin.last n)) hlast
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)), Eq.{u1} (C (Fin.last n)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) hlast hcast (Fin.last n)) hlast
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)), Eq.{u1} (C (Fin.last n)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C _x) hlast hcast (Fin.last n)) hlast
 Case conversion may be inaccurate. Consider using '#align fin.last_cases_last Fin.lastCases_lastₓ'. -/
 @[simp]
 theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
@@ -2963,7 +2963,7 @@ theorem lastCases_last {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.la
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (i : Fin n), Eq.{u1} ((fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (Fin.lastCases.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) hlast hcast (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (hcast i)
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (hlast : C (Fin.last n)) (hcast : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (Fin.lastCases.{u1} n C hlast hcast (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (hcast i)
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(RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (Fin.lastCases.{u1} n C hlast hcast (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (hcast i)
 Case conversion may be inaccurate. Consider using '#align fin.last_cases_cast_succ Fin.lastCases_castSuccₓ'. -/
 @[simp]
 theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fin.last n))
@@ -2976,7 +2976,7 @@ theorem lastCases_castSucc {n : ℕ} {C : Fin (n + 1) → Sort _} (hlast : C (Fi
 lean 3 declaration is
   forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) -> Sort.{u1}}, (forall (i : Fin m), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) -> (forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)), C i)
 but is expected to have type
-  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}}, (forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd m n)) i)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)), C i)
+  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}}, (forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) -> (forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)), C i)
 Case conversion may be inaccurate. Consider using '#align fin.add_cases Fin.addCasesₓ'. -/
 /-- Define `f : Π i : fin (m + n), C i` by separately handling the cases `i = cast_add n i`,
 `j : fin m` and `i = nat_add m j`, `j : fin n`. -/
@@ -2991,7 +2991,7 @@ def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd
 lean 3 declaration is
   forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) (hright : forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) (i : Fin m), Eq.{u1} (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) (Fin.addCases.{u1} m n C hleft hright (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) (hleft i)
 but is expected to have type
-  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd m n)) i)) (hright : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) i)) (i : Fin m), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd m n)) i)) (Fin.addCases.{u1} m n C hleft hright (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd m n)) i)) (hleft i)
+  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) (hright : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)) (i : Fin m), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) (Fin.addCases.{u1} m n C hleft hright (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) (hleft i)
 Case conversion may be inaccurate. Consider using '#align fin.add_cases_left Fin.addCases_leftₓ'. -/
 @[simp]
 theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
@@ -3007,7 +3007,7 @@ theorem addCases_left {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C
 lean 3 declaration is
   forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe m) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin m) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.castAdd m n) i)) (hright : forall (i : Fin n), C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) (i : Fin n), Eq.{u1} (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) (Fin.addCases.{u1} m n C hleft hright (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m n)))) (Fin.natAdd m n) i)) (hright i)
 but is expected to have type
-  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd m n)) i)) (hright : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) i)) (Fin.addCases.{u1} m n C hleft hright (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.natAdd m n)) i)) (hright i)
+  forall {m : Nat} {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) -> Sort.{u1}} (hleft : forall (i : Fin m), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin m) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin m) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin m) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castAdd m n) i)) (hright : forall (i : Fin n), C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)) (i : Fin n), Eq.{u1} (C (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)) (Fin.addCases.{u1} m n C hleft hright (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m n)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.natAdd m n) i)) (hright i)
 Case conversion may be inaccurate. Consider using '#align fin.add_cases_right Fin.addCases_rightₓ'. -/
 @[simp]
 theorem addCases_right {m n : ℕ} {C : Fin (m + n) → Sort _} (hleft : ∀ i, C (castAdd n i))
@@ -3027,7 +3027,7 @@ end Rec
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α α (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) r f f) (forall (i : Fin n), r (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15362 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15364 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15362 x._@.Mathlib.Data.Fin.Basic._hyg.15364) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15356 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15358 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15356 x._@.Mathlib.Data.Fin.Basic._hyg.15358) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=
@@ -3047,7 +3047,7 @@ theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r]
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictMono.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.strict_mono_iff_lt_succ Fin.strictMono_iff_lt_succₓ'. -/
 /-- A function `f` on `fin (n + 1)` is strictly monotone if and only if `f i < f (i + 1)`
 for all `i`. -/
@@ -3060,7 +3060,7 @@ theorem strictMono_iff_lt_succ {α : Type _} [Preorder α] {f : Fin (n + 1) →
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Monotone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.monotone_iff_le_succ Fin.monotone_iff_le_succₓ'. -/
 /-- A function `f` on `fin (n + 1)` is monotone if and only if `f i ≤ f (i + 1)` for all `i`. -/
 theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
@@ -3072,7 +3072,7 @@ theorem monotone_iff_le_succ {α : Type _} [Preorder α] {f : Fin (n + 1) → α
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (StrictAnti.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.strict_anti_iff_succ_lt Fin.strictAnti_iff_succ_ltₓ'. -/
 /-- A function `f` on `fin (n + 1)` is strictly antitone if and only if `f (i + 1) < f i`
 for all `i`. -/
@@ -3085,7 +3085,7 @@ theorem strictAnti_iff_succ_lt {α : Type _} [Preorder α] {f : Fin (n + 1) →
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (Fin.succ n i)) (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
+  forall {n : Nat} {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Antitone.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) _inst_1 f) (forall (i : Fin n), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (f (Fin.succ n i)) (f (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)))
 Case conversion may be inaccurate. Consider using '#align fin.antitone_iff_succ_le Fin.antitone_iff_succ_leₓ'. -/
 /-- A function `f` on `fin (n + 1)` is antitone if and only if `f (i + 1) ≤ f i` for all `i`. -/
 theorem antitone_iff_succ_le {α : Type _} [Preorder α] {f : Fin (n + 1) → α} :
@@ -3256,7 +3256,7 @@ section SuccAbove
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), StrictMono.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (i : Fin n) => ite.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat 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(instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) (Fin.decLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_aux Fin.succAbove_auxₓ'. -/
 theorem succAbove_aux (p : Fin (n + 1)) :
     StrictMono fun i : Fin n => if i.cast_succ < p then i.cast_succ else i.succ :=
@@ -3280,7 +3280,7 @@ def succAbove (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
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(instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i) p) -> (Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n p)) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} 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+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_below Fin.succAbove_belowₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `cast_succ` when the resulting `i.cast_succ < p`. -/
@@ -3294,7 +3294,7 @@ theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : i.cast_succ < p) :
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n a)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zeroₓ'. -/
 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 :=
@@ -3308,7 +3308,7 @@ theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.s
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Iff (Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n a)) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Eq.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iffₓ'. -/
 theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) :
     a.succAbove b = 0 ↔ b = 0 := by
@@ -3319,7 +3319,7 @@ theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a 
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) -> (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) -> (Ne.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n a)) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {b : Fin n}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) -> (Ne.{1} (Fin n) b (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) -> (Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n a) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) b) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne_zero Fin.succAbove_ne_zeroₓ'. -/
 theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) (hb : b ≠ 0) :
     a.succAbove b ≠ 0 :=
@@ -3330,7 +3330,7 @@ theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} ((Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))) (Fin.succ n)
 but is expected to have type
-  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))))) (Fin.succ n)
+  forall {n : Nat}, Eq.{1} (forall (ᾰ : Fin n), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ᾰ) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (Fin.succ n)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_zero Fin.succAbove_zeroₓ'. -/
 /-- Embedding `fin n` into `fin (n + 1)` with a hole around zero embeds by `succ`. -/
 @[simp]
@@ -3356,7 +3356,7 @@ theorem succAbove_last : succAbove (Fin.last n) = castSucc :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.last n)) i) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n (Fin.last n))) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)
+  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (Fin.last n)) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_last_apply Fin.succAbove_last_applyₓ'. -/
 theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_succ := by
   rw [succ_above_last]
@@ -3366,7 +3366,7 @@ theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = i.cast_suc
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n p)) i) (Fin.succ n i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i)) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i) (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_above Fin.succAbove_aboveₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
@@ -3378,7 +3378,7 @@ theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ i.cast_succ) :
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Or (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i) p) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_ge Fin.succAbove_lt_geₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p ≤ i.cast_succ :=
@@ -3389,7 +3389,7 @@ theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p 
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Or (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (Fin.succ n i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i) p) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (Fin.succ n i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Or (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p) (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (Fin.succ n i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_gt Fin.succAbove_lt_gtₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` is always about some hole `p`. -/
 theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p < i.succ :=
@@ -3401,7 +3401,7 @@ theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : i.cast_succ < p ∨ p <
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder 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(One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) p)
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n p)) i) p) (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i) p)
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i) p) (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i) p)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_lt_iff Fin.succAbove_lt_iffₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
@@ -3423,7 +3423,7 @@ theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ i
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n p)) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Iff (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) i))
 Case conversion may be inaccurate. Consider using '#align fin.lt_succ_above_iff Fin.lt_succAbove_iffₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
@@ -3444,7 +3444,7 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i) p
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Ne.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n p)) i) p
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), Ne.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i) p
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_ne Fin.succAbove_neₓ'. -/
 /-- Embedding `i : fin n` into `fin (n + 1)` with a hole around `p : fin (n + 1)`
 never results in `p` itself -/
@@ -3460,7 +3460,7 @@ theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p :=
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin n), (LT.lt.{0} (Fin n) (Fin.hasLt n) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1)))) i) -> (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p) i))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n p)) i))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin n), (LT.lt.{0} (Fin n) (instLTFin n) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1)) i) -> (LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p) i))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pos Fin.succAbove_posₓ'. -/
 /-- Embedding a positive `fin n` results in a positive fin (n + 1)` -/
 theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i :=
@@ -3474,7 +3474,7 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hx : optParam.{0} (LT.lt.{0} Nat (Preorder.toLT.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) y) n h (Fin.le_last n y))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x hx)) x
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hx : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n h (Fin.le_last n y))), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) x
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hx : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n h (Fin.le_last n y))), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) x
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_cast_lt Fin.succAbove_castLTₓ'. -/
 @[simp]
 theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
@@ -3488,7 +3488,7 @@ theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hy : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (LT.lt.ne'.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) y (LE.le.trans_lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) x y (Fin.zero_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (NeZero.succ n) x) h))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) (Fin.pred n y hy)) y
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hy : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (LT.lt.ne'.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) y (LE.le.trans_lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) x y (Fin.zero_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n) x) h))), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.pred n y hy)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n x)) (Fin.pred n y hy)) y
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hy : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (LT.lt.ne'.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) y (LE.le.trans_lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) x y (Fin.zero_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n) x) h))), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.pred n y hy)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) (Fin.pred n y hy)) y
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred Fin.succAbove_predₓ'. -/
 @[simp]
 theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') :
@@ -3502,7 +3502,7 @@ theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.cast_lt_succ_above Fin.castLT_succAboveₓ'. -/
 theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
     (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
@@ -3513,7 +3513,7 @@ theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
 lean 3 declaration is
   forall {n : Nat} {x : Fin n} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) x)) (h' : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : 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 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above Fin.pred_succAboveₓ'. -/
 theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
     (h' : y.succAbove x ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
@@ -3524,7 +3524,7 @@ theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) z) x))
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) z) x))
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) -> (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n y) z) x))
 Case conversion may be inaccurate. Consider using '#align fin.exists_succ_above_eq Fin.exists_succAbove_eqₓ'. -/
 theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x :=
   by
@@ -3536,7 +3536,7 @@ theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbo
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) y x)
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n x)) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y x)
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Exists.{1} (Fin n) (fun (z : Fin n) => Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) z) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) z) y)) (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) y x)
 Case conversion may be inaccurate. Consider using '#align fin.exists_succ_above_eq_iff Fin.exists_succAbove_eq_iffₓ'. -/
 @[simp]
 theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y) ↔ y ≠ x :=
@@ -3550,7 +3550,7 @@ theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y)
 lean 3 declaration is
   forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n p))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.booleanAlgebra.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Set.hasSingleton.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) p))
 but is expected to have type
-  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n p)))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instBooleanAlgebraSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instSingletonSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) p))
+  forall {n : Nat} (p : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n p))) (HasCompl.compl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (BooleanAlgebra.toHasCompl.{0} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instBooleanAlgebraSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Singleton.singleton.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instSingletonSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) p))
 Case conversion may be inaccurate. Consider using '#align fin.range_succ_above Fin.range_succAboveₓ'. -/
 /-- The range of `p.succ_above` is everything except `p`. -/
 @[simp]
@@ -3584,7 +3584,7 @@ theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠
 lean 3 declaration is
   forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x))
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n x)))
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Function.Injective.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x))
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_right_injective Fin.succAbove_right_injectiveₓ'. -/
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
@@ -3595,7 +3595,7 @@ theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
 lean 3 declaration is
   forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))}, Iff (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) a) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
 but is expected to have type
-  forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n x)) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n x)) b)) (Eq.{1} (Fin n) a b)
+  forall {n : Nat} {a : Fin n} {b : Fin n} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))}, Iff (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) a) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n x) b)) (Eq.{1} (Fin n) a b)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_right_inj Fin.succAbove_right_injₓ'. -/
 /-- Given a fixed pivot `x : fin (n + 1)`, `x.succ_above` is injective -/
 theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b ↔ a = b :=
@@ -3629,7 +3629,7 @@ theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAbove = y.succAbove ↔ x
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) i) (Fin.succ n i)
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) i) (Fin.succ n i)
+  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) i) (Fin.succ n i)
 Case conversion may be inaccurate. Consider using '#align fin.zero_succ_above Fin.zero_succAboveₓ'. -/
 @[simp]
 theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i.succ :=
@@ -3640,7 +3640,7 @@ theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i
 lean 3 declaration is
   forall {n : Nat} [_inst_1 : NeZero.{0} Nat Nat.hasZero n] (i : Fin n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n (Fin.succ n i))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (Fin.succ n i)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_zero Fin.succ_succAbove_zeroₓ'. -/
 @[simp]
 theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove 0 = 0 :=
@@ -3651,7 +3651,7 @@ theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : i.succ.succAbove
 lean 3 declaration is
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Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i)) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} 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Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n i) j))
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (j : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ n j)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (fun (_x : Fin (Nat.succ (Nat.add n 0))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ (Nat.add n 0))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ (Nat.add n 0))) => LE.le.{0} (Fin (Nat.succ (Nat.add n 0))) (instLEFin (Nat.succ (Nat.add n 0))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove (Nat.succ (Nat.add n 0)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n i)) j))
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (j : Fin n), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ n j)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ (Nat.add n 0))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (fun (_x : Fin (Nat.succ (Nat.add n 0))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ (Nat.add n 0))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ (Nat.add n 0))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ (Nat.add n 0))) => LE.le.{0} (Fin (Nat.succ (Nat.add n 0))) (instLEFin (Nat.succ (Nat.add n 0))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ (Nat.add n 0))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ (Nat.add n 0))) => LE.le.{0} (Fin (Nat.succ (Nat.add n 0))) (instLEFin (Nat.succ (Nat.add n 0))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove (Nat.succ (Nat.add n 0)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (Fin.succ n j)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n i) j))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_succ Fin.succ_succAbove_succₓ'. -/
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
@@ -3671,7 +3671,7 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
 lean 3 declaration is
   forall {n : Nat}, Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 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 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_zero Fin.one_succAbove_zeroₓ'. -/
 @[simp]
 theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
@@ -3682,7 +3682,7 @@ theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 :=
 lean 3 declaration is
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-> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n i) (OfNat.ofNat.{0} (Fin n) 0 (OfNat.mk.{0} (Fin n) 0 (Zero.zero.{0} (Fin n) (Fin.hasZeroOfNeZero n _inst_1))))))
 but is expected to have type
-  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin (Nat.succ (Nat.add n 0))) 1 (Fin.instOfNatFin (Nat.succ (Nat.add n 0)) 1 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (fun (_x : Fin (Nat.succ (Nat.add n 0))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ (Nat.add n 0))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ (Nat.add n 0))) => LE.le.{0} (Fin (Nat.succ (Nat.add n 0))) (instLEFin (Nat.succ (Nat.add n 0))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove (Nat.succ (Nat.add n 0)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i))) (OfNat.ofNat.{0} (Fin (Nat.succ (Nat.add n 0))) 1 (Fin.instOfNatFin (Nat.succ (Nat.add n 0)) 1 (NeZero.succ n)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n i)) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
+  forall {n : Nat} [_inst_1 : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n] (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin (Nat.succ (Nat.add n 0))) 1 (Fin.instOfNatFin (Nat.succ (Nat.add n 0)) 1 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ (Nat.add n 0))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (fun (_x : Fin (Nat.succ (Nat.add n 0))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (Nat.succ (Nat.add n 0))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (Nat.succ (Nat.add n 0))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ (Nat.add n 0))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ (Nat.add n 0))) => LE.le.{0} (Fin (Nat.succ (Nat.add n 0))) (instLEFin (Nat.succ (Nat.add n 0))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (Nat.succ (Nat.add n 0))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ (Nat.add n 0))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ (Nat.add n 0))) => LE.le.{0} (Fin (Nat.succ (Nat.add n 0))) (instLEFin (Nat.succ (Nat.add n 0))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Nat.succ (Nat.add n 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove (Nat.succ (Nat.add n 0)) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (OfNat.ofNat.{0} (Fin (Nat.succ (Nat.add n 0))) 1 (Fin.instOfNatFin (Nat.succ (Nat.add n 0)) 1 (NeZero.succ n)))) (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n i) (OfNat.ofNat.{0} (Fin n) 0 (Fin.instOfNatFin n 0 _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin.succ_succ_above_one Fin.succ_succAbove_oneₓ'. -/
 /-- By moving `succ` to the outside of this expression, we create opportunities for further
 simplification using `succ_above_zero` or `succ_succ_above_zero`. -/
@@ -3696,7 +3696,7 @@ theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_succ Fin.one_succAbove_succₓ'. -/
 @[simp]
 theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j.succ = j.succ.succ :=
@@ -3707,7 +3707,7 @@ theorem one_succAbove_succ {n : ℕ} (j : Fin n) : (1 : Fin (n + 2)).succAbove j
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align fin.one_succ_above_one Fin.one_succAbove_oneₓ'. -/
 @[simp]
 theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 :=
@@ -3837,7 +3837,7 @@ theorem coe_castPred {n : ℕ} (a : Fin (n + 2)) (hx : a < Fin.last _) : (a.cast
 lean 3 declaration is
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 but is expected to have type
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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) p i) (Fin.castPred n i))
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_below Fin.predAbove_belowₓ'. -/
 theorem predAbove_below (p : Fin (n + 1)) (i : Fin (n + 2)) (h : i ≤ p.cast_succ) :
     p.predAbove i = i.cast_pred :=
@@ -3867,7 +3867,7 @@ theorem predAbove_last_apply (i : Fin n) : predAbove (Fin.last n) i = i.cast_pre
 lean 3 declaration is
   forall {n : Nat} (p : Fin n) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p) i), Eq.{1} (Fin n) (Fin.predAbove n p i) (Fin.pred n i (Ne.symm.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) i (LT.lt.ne.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) i (LE.le.trans_lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p) i (Fin.zero_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (NeZero.succ n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat 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(Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) h))))
 but is expected to have type
-  forall {n : Nat} (p : Fin n) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 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0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) p) i (Fin.zero_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} 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+  forall {n : Nat} (p : Fin n) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p) i), Eq.{1} (Fin n) (Fin.predAbove n p i) (Fin.pred n i (Ne.symm.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) i (LT.lt.ne.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) i (LE.le.trans_lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instPartialOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Zero.toOfNat0.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instZeroFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p) i (Fin.zero_le (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) h))))
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_above Fin.predAbove_aboveₓ'. -/
 theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : p.cast_succ < i) :
     p.predAbove i = i.pred (p.cast_succ.zero_le.trans_lt h).Ne.symm := by simp [pred_above, h]
@@ -3887,7 +3887,7 @@ theorem castPred_monotone : Monotone (@castPred n) :=
 lean 3 declaration is
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(LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) (Fin.predAbove n p i)) i)
 but is expected to have type
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1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) p))) (Fin.predAbove n p i)) i)
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x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) -> (Eq.{1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.predAbove n p i)) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) (Fin.predAbove n p i)) i)
 Case conversion may be inaccurate. Consider using '#align fin.succ_above_pred_above Fin.succAbove_predAboveₓ'. -/
 /-- Sending `fin (n+1)` to `fin n` by subtracting one from anything above `p`
 then back to `fin (n+1)` with a gap around `p` is the identity away from `p`. -/
@@ -3920,7 +3920,7 @@ theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ p.cast_succ
 lean 3 declaration is
   forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) p)) i)) i
 but is expected to have type
-  forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) p))) i)) i
+  forall {n : Nat} (p : Fin n) (i : Fin n), Eq.{1} (Fin n) (Fin.predAbove n p (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.succAbove n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc n) p)) i)) i
 Case conversion may be inaccurate. Consider using '#align fin.pred_above_succ_above Fin.predAbove_succAboveₓ'. -/
 /-- Sending `fin n` into `fin (n + 1)` with a gap at `p`
 then back to `fin n` by subtracting one from anything above `p` is the identity. -/
@@ -3946,7 +3946,7 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) : p.predAbove (p.cast_succ.s
 lean 3 declaration is
   forall {n : Nat} {a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (ha : Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) a (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (ha' : optParam.{0} (Ne.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 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(OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 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 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSuccₓ'. -/
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
     (ha' := a.castSucc_ne_zero_iff.mpr ha) : (a.pred ha).cast_succ = a.cast_succ.pred ha' :=
@@ -3959,7 +3959,7 @@ theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align fin.pred_succ_above_pred Fin.pred_succAbove_predₓ'. -/
 /-- `pred` commutes with `succ_above`. -/
 theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
@@ -4010,7 +4010,7 @@ theorem succ_predAbove_succ (a : Fin n) (b : Fin (n + 1)) :
 lean 3 declaration is
   forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.castPred n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) i)) i
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) i)) i
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (RelHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)) i
 Case conversion may be inaccurate. Consider using '#align fin.cast_pred_cast_succ Fin.castPred_castSuccₓ'. -/
 @[simp]
 theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
@@ -4021,7 +4021,7 @@ theorem castPred_castSucc (i : Fin (n + 1)) : castPred i.cast_succ = i := by
 lean 3 declaration is
   forall {n : Nat} {i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))}, (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) i (Fin.last (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) -> (Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat 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 but is expected to have type
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(x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Fin.castSucc (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castPred n i)) i)
 Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_pred Fin.castSucc_castPredₓ'. -/
 theorem castSucc_castPred {i : Fin (n + 2)} (h : i < last _) : castSucc i.cast_pred = i :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -4168,13 +4168,13 @@ section
 -- the expression we use here is equivalent.
 attribute [local semireducible] reflected
 
-unsafe instance reflect : ∀ n, has_reflect (Fin n)
+unsafe instance toExpr : ∀ n, has_reflect (Fin n)
   | 0 => finZeroElim
   | n + 1 =>
     nat.mk_numeral q(Fin n.succ) q((by infer_instance : Zero (Fin n.succ)))
         q((by infer_instance : One (Fin n.succ))) q((by infer_instance : Add (Fin n.succ))) ∘
       Fin.val
-#align fin.reflect fin.reflect
+#align fin.reflect Fin.toExprₓ
 
 end
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -1472,111 +1472,111 @@ theorem castLT_mk (i n m : ℕ) (hn : i < n) (hm : i < m) : castLT ⟨i, hn⟩ h
 #align fin.cast_lt_mk Fin.castLT_mk
 -/
 
-#print Fin.castLe /-
+#print Fin.castLE /-
 /-- `cast_le h i` embeds `i` into a larger `fin` type.  -/
-def castLe (h : n ≤ m) : Fin n ↪o Fin m :=
+def castLE (h : n ≤ m) : Fin n ↪o Fin m :=
   OrderEmbedding.ofStrictMono (fun a => castLT a (lt_of_lt_of_le a.2 h)) fun a b h => h
-#align fin.cast_le Fin.castLe
+#align fin.cast_le Fin.castLE
 -/
 
-/- warning: fin.coe_cast_le -> Fin.coe_castLe is a dubious translation:
+/- warning: fin.coe_cast_le -> Fin.coe_castLE is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe n m) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLe n m h) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe n m) (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin m) Nat (HasLiftT.mk.{1, 1} (Fin m) Nat (CoeTCₓ.coe.{1, 1} (Fin m) Nat (coeBase.{1, 1} (Fin m) Nat (Fin.coeToNat m)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE n m h) i)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i)
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n m h)) i)) (Fin.val n i)
-Case conversion may be inaccurate. Consider using '#align fin.coe_cast_le Fin.coe_castLeₓ'. -/
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat n m) (i : Fin n), Eq.{1} Nat (Fin.val m (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n m h)) i)) (Fin.val n i)
+Case conversion may be inaccurate. Consider using '#align fin.coe_cast_le Fin.coe_castLEₓ'. -/
 @[simp]
-theorem coe_castLe (h : n ≤ m) (i : Fin n) : (castLe h i : ℕ) = i :=
+theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : ℕ) = i :=
   rfl
-#align fin.coe_cast_le Fin.coe_castLe
+#align fin.coe_cast_le Fin.coe_castLE
 
-/- warning: fin.cast_le_mk -> Fin.castLe_mk is a dubious translation:
+/- warning: fin.cast_le_mk -> Fin.castLE_mk is a dubious translation:
 lean 3 declaration is
-  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat Nat.hasLt i n) (h : LE.le.{0} Nat Nat.hasLe n m), Eq.{1} (Fin m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLe n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) i n m hn h))
+  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat Nat.hasLt i n) (h : LE.le.{0} Nat Nat.hasLe n m), Eq.{1} (Fin m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE n m h) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) i n m hn h))
 but is expected to have type
-  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat instLTNat i n) (h : LE.le.{0} Nat instLENat n m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) (Fin.mk n i hn)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n m h)) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn h))
-Case conversion may be inaccurate. Consider using '#align fin.cast_le_mk Fin.castLe_mkₓ'. -/
+  forall (i : Nat) (n : Nat) (m : Nat) (hn : LT.lt.{0} Nat instLTNat i n) (h : LE.le.{0} Nat instLENat n m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) (Fin.mk n i hn)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n m h)) (Fin.mk n i hn)) (Fin.mk m i (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) i n m hn h))
+Case conversion may be inaccurate. Consider using '#align fin.cast_le_mk Fin.castLE_mkₓ'. -/
 @[simp]
-theorem castLe_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
-    castLe h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h⟩ :=
+theorem castLE_mk (i n m : ℕ) (hn : i < n) (h : n ≤ m) :
+    castLE h ⟨i, hn⟩ = ⟨i, lt_of_lt_of_le hn h⟩ :=
   rfl
-#align fin.cast_le_mk Fin.castLe_mk
+#align fin.cast_le_mk Fin.castLE_mk
 
-/- warning: fin.cast_le_zero -> Fin.castLe_zero is a dubious translation:
+/- warning: fin.cast_le_zero -> Fin.castLE_zero is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe (Nat.succ n) (Nat.succ m)), Eq.{1} (Fin (Nat.succ m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ m))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) (Fin.castLe (Nat.succ n) (Nat.succ m) h) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (OfNat.mk.{0} (Fin (Nat.succ n)) 0 (Zero.zero.{0} (Fin (Nat.succ n)) (Fin.hasZeroOfNeZero (Nat.succ n) (NeZero.succ n)))))) (OfNat.ofNat.{0} (Fin (Nat.succ m)) 0 (OfNat.mk.{0} (Fin (Nat.succ m)) 0 (Zero.zero.{0} (Fin (Nat.succ m)) (Fin.hasZeroOfNeZero (Nat.succ m) (NeZero.succ m)))))
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat Nat.hasLe (Nat.succ n) (Nat.succ m)), Eq.{1} (Fin (Nat.succ m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ n)) (Fin.hasLe (Nat.succ m))) (fun (_x : RelEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) => (Fin (Nat.succ n)) -> (Fin (Nat.succ m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (LE.le.{0} (Fin (Nat.succ n)) (Fin.hasLe (Nat.succ n))) (LE.le.{0} (Fin (Nat.succ m)) (Fin.hasLe (Nat.succ m)))) (Fin.castLE (Nat.succ n) (Nat.succ m) h) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (OfNat.mk.{0} (Fin (Nat.succ n)) 0 (Zero.zero.{0} (Fin (Nat.succ n)) (Fin.hasZeroOfNeZero (Nat.succ n) (NeZero.succ n)))))) (OfNat.ofNat.{0} (Fin (Nat.succ m)) 0 (OfNat.mk.{0} (Fin (Nat.succ m)) 0 (Zero.zero.{0} (Fin (Nat.succ m)) (Fin.hasZeroOfNeZero (Nat.succ m) (NeZero.succ m)))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat (Nat.succ n) (Nat.succ m)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m))) (Fin (Nat.succ n)) (Fin (Nat.succ m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe (Nat.succ n) (Nat.succ m) h)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) 0 (Fin.instOfNatFin (Nat.succ m) 0 (NeZero.succ m)))
-Case conversion may be inaccurate. Consider using '#align fin.cast_le_zero Fin.castLe_zeroₓ'. -/
+  forall {n : Nat} {m : Nat} (h : LE.le.{0} Nat instLENat (Nat.succ n) (Nat.succ m)), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m))) (Fin (Nat.succ n)) (fun (_x : Fin (Nat.succ n)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m))) (Fin (Nat.succ n)) (Fin (Nat.succ m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (Nat.succ n)) (Fin (Nat.succ m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin (Nat.succ n)) (Fin (Nat.succ m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (Nat.succ n)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (Nat.succ n)) => LE.le.{0} (Fin (Nat.succ n)) (instLEFin (Nat.succ n)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (Nat.succ m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (Nat.succ m)) => LE.le.{0} (Fin (Nat.succ m)) (instLEFin (Nat.succ m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE (Nat.succ n) (Nat.succ m) h)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (Nat.succ n)) => Fin (Nat.succ m)) (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n)))) 0 (Fin.instOfNatFin (Nat.succ m) 0 (NeZero.succ m)))
+Case conversion may be inaccurate. Consider using '#align fin.cast_le_zero Fin.castLE_zeroₓ'. -/
 @[simp]
-theorem castLe_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLe h 0 = 0 := by simp [eq_iff_veq]
-#align fin.cast_le_zero Fin.castLe_zero
+theorem castLE_zero {n m : ℕ} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [eq_iff_veq]
+#align fin.cast_le_zero Fin.castLE_zero
 
-/- warning: fin.range_cast_le -> Fin.range_castLe is a dubious translation:
+/- warning: fin.range_cast_le -> Fin.range_castLE is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (Fin.hasLe n) (Fin.hasLe k)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i) n))
+  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin k) (Fin.hasLe n) (Fin.hasLe k)) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i) n))
 but is expected to have type
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h)))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat instLTNat (Fin.val k i) n))
-Case conversion may be inaccurate. Consider using '#align fin.range_cast_le Fin.range_castLeₓ'. -/
+  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k), Eq.{1} (Set.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h)))) (setOf.{0} (Fin k) (fun (i : Fin k) => LT.lt.{0} Nat instLTNat (Fin.val k i) n))
+Case conversion may be inaccurate. Consider using '#align fin.range_cast_le Fin.range_castLEₓ'. -/
 @[simp]
-theorem range_castLe {n k : ℕ} (h : n ≤ k) : Set.range (castLe h) = { i | (i : ℕ) < n } :=
+theorem range_castLE {n k : ℕ} (h : n ≤ k) : Set.range (castLE h) = { i | (i : ℕ) < n } :=
   Set.ext fun x => ⟨fun ⟨y, hy⟩ => hy ▸ y.2, fun hx => ⟨⟨x, hx⟩, Fin.ext rfl⟩⟩
-#align fin.range_cast_le Fin.range_castLe
+#align fin.range_cast_le Fin.range_castLE
 
-/- warning: fin.coe_of_injective_cast_le_symm -> Fin.coe_of_injective_castLe_symm is a dubious translation:
+/- warning: fin.coe_of_injective_cast_le_symm -> Fin.coe_of_injective_castLE_symm is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k) (i : Fin k) (hi : Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Fin n)) => (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k)) (Fin.castLe n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) i hi))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i)
+  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k) (i : Fin k) (hi : Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) => (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k)) (Fin.castLE n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLE n k h)))) i hi))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i)
 but is expected to have type
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k) (i : Fin k) (hi : Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Fin n)) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (fun (_x : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 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(EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) i hi))) (Fin.val k i)
-Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLe_symmₓ'. -/
+  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k) (i : Fin k) (hi : Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) (Fin n)) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) (fun (_x : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE n k h))))) i hi))) (Fin.val k i)
+Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symmₓ'. -/
 @[simp]
-theorem coe_of_injective_castLe_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
-    ((Equiv.ofInjective _ (castLe h).Injective).symm ⟨i, hi⟩ : ℕ) = i :=
+theorem coe_of_injective_castLE_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
+    ((Equiv.ofInjective _ (castLE h).Injective).symm ⟨i, hi⟩ : ℕ) = i :=
   by
   rw [← coe_cast_le]
   exact congr_arg coe (Equiv.apply_ofInjective_symm _ _)
-#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLe_symm
+#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLE_symm
 
-/- warning: fin.cast_le_succ -> Fin.castLe_succ is a dubious translation:
+/- warning: fin.cast_le_succ -> Fin.castLE_succ is a dubious translation:
 lean 3 declaration is
-  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat Nat.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) (Fin.succ m i)) (Fin.succ n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLe m n (Iff.mp (LE.le.{0} Nat Nat.hasLe (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe m n) (Nat.succ_le_succ_iff m n) h)) i))
+  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat Nat.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin m), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) (Fin.succ m i)) (Fin.succ n (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat Nat.hasLe (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe m n) (Nat.succ_le_succ_iff m n) h)) i))
 but is expected to have type
-  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat instLENat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ m i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h)) (Fin.succ m i)) (Fin.succ n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe m n (Iff.mp (LE.le.{0} Nat instLENat (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat instLENat m n) (Nat.succ_le_succ_iff m n) h))) i))
-Case conversion may be inaccurate. Consider using '#align fin.cast_le_succ Fin.castLe_succₓ'. -/
+  forall {m : Nat} {n : Nat} (h : LE.le.{0} Nat instLENat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin m), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.succ m i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h)) (Fin.succ m i)) (Fin.succ n (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n (Iff.mp (LE.le.{0} Nat instLENat (Nat.succ m) (Nat.succ n)) (LE.le.{0} Nat instLENat m n) (Nat.succ_le_succ_iff m n) h))) i))
+Case conversion may be inaccurate. Consider using '#align fin.cast_le_succ Fin.castLE_succₓ'. -/
 @[simp]
-theorem castLe_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
-    castLe h i.succ = (castLe (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.eq_iff_veq]
-#align fin.cast_le_succ Fin.castLe_succ
+theorem castLE_succ {m n : ℕ} (h : m + 1 ≤ n + 1) (i : Fin m) :
+    castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.eq_iff_veq]
+#align fin.cast_le_succ Fin.castLE_succ
 
-/- warning: fin.cast_le_cast_le -> Fin.castLe_castLe is a dubious translation:
+/- warning: fin.cast_le_cast_le -> Fin.castLE_castLE is a dubious translation:
 lean 3 declaration is
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n) (i : Fin k), Eq.{1} (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLe m n mn) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLe k m km) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLe k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)) i)
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n) (i : Fin k), Eq.{1} (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n mn) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE k m km) i)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)) i)
 but is expected to have type
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n) (i : Fin k), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (a : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe k m km)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe m n mn)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe k m km)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn))) i)
-Case conversion may be inaccurate. Consider using '#align fin.cast_le_cast_le Fin.castLe_castLeₓ'. -/
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n) (i : Fin k), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (a : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k m km)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n mn)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k m km)) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn))) i)
+Case conversion may be inaccurate. Consider using '#align fin.cast_le_cast_le Fin.castLE_castLEₓ'. -/
 @[simp]
-theorem castLe_castLe {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
-    Fin.castLe mn (Fin.castLe km i) = Fin.castLe (km.trans mn) i :=
+theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
+    Fin.castLE mn (Fin.castLE km i) = Fin.castLE (km.trans mn) i :=
   Fin.ext (by simp only [coe_cast_le])
-#align fin.cast_le_cast_le Fin.castLe_castLe
+#align fin.cast_le_cast_le Fin.castLE_castLE
 
-/- warning: fin.cast_le_comp_cast_le -> Fin.castLe_comp_castLe is a dubious translation:
+/- warning: fin.cast_le_comp_cast_le -> Fin.castLE_comp_castLE is a dubious translation:
 lean 3 declaration is
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLe m n mn)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLe k m km))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLe k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)))
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat Nat.hasLe k m) (mn : LE.le.{0} Nat Nat.hasLe m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n mn)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin m) (Fin.hasLe k) (Fin.hasLe m)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin k) -> (Fin m)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin m) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.castLE k m km))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin k) (Fin n) (Fin.hasLe k) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin k) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin k) (Fin n) (LE.le.{0} (Fin k) (Fin.hasLe k)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k m n km mn)))
 but is expected to have type
-  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe m n mn))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe k m km)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn))))
-Case conversion may be inaccurate. Consider using '#align fin.cast_le_comp_cast_le Fin.castLe_comp_castLeₓ'. -/
+  forall {k : Nat} {m : Nat} {n : Nat} (km : LE.le.{0} Nat instLENat k m) (mn : LE.le.{0} Nat instLENat m n), Eq.{1} ((Fin k) -> (Fin n)) (Function.comp.{1, 1, 1} (Fin k) (Fin m) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n mn))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin m)) (Fin k) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k m km)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (fun (_x : Fin k) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin k) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin k) (Fin n)) (Fin k) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin k) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin k) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE k n (LE.le.trans.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k m n km mn))))
+Case conversion may be inaccurate. Consider using '#align fin.cast_le_comp_cast_le Fin.castLE_comp_castLEₓ'. -/
 @[simp]
-theorem castLe_comp_castLe {k m n} (km : k ≤ m) (mn : m ≤ n) :
-    Fin.castLe mn ∘ Fin.castLe km = Fin.castLe (km.trans mn) :=
-  funext (castLe_castLe km mn)
-#align fin.cast_le_comp_cast_le Fin.castLe_comp_castLe
+theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
+    Fin.castLE mn ∘ Fin.castLE km = Fin.castLE (km.trans mn) :=
+  funext (castLE_castLE km mn)
+#align fin.cast_le_comp_cast_le Fin.castLE_comp_castLE
 
 #print Fin.cast /-
 /-- `cast eq i` embeds `i` into a equal `fin` type, see also `equiv.fin_congr`. -/
 def cast (eq : n = m) : Fin n ≃o Fin m
     where
-  toEquiv := ⟨castLe Eq.le, castLe Eq.symm.le, fun a => eq_of_veq rfl, fun a => eq_of_veq rfl⟩
+  toEquiv := ⟨castLE Eq.le, castLE Eq.symm.le, fun a => eq_of_veq rfl, fun a => eq_of_veq rfl⟩
   map_rel_iff' a b := Iff.rfl
 #align fin.cast Fin.cast
 -/
@@ -1658,16 +1658,16 @@ theorem cast_refl (h : n = n := rfl) : cast h = OrderIso.refl (Fin n) :=
 #align fin.cast_refl Fin.cast_refl
 -/
 
-/- warning: fin.cast_le_of_eq -> Fin.castLe_of_eq is a dubious translation:
+/- warning: fin.cast_le_of_eq -> Fin.castLE_of_eq is a dubious translation:
 lean 3 declaration is
-  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat Nat.hasLe m n}, Eq.{1} ((fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (Fin.castLe m n h')) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLe m n h')) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast m n h))
+  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat Nat.hasLe m n}, Eq.{1} ((fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (Fin.castLE m n h')) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelEmbedding.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.castLE m n h')) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin m) (Fin n) (Fin.hasLe m) (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin m) -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin m) (Fin n) (LE.le.{0} (Fin m) (Fin.hasLe m)) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast m n h))
 but is expected to have type
-  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat instLENat m n}, Eq.{1} (forall (a : Fin m), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe m n h'))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast m n h))))
-Case conversion may be inaccurate. Consider using '#align fin.cast_le_of_eq Fin.castLe_of_eqₓ'. -/
-theorem castLe_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
-    (castLe h' : Fin m → Fin n) = Fin.cast h :=
+  forall {m : Nat} {n : Nat} (h : Eq.{1} Nat m n) {h' : LE.le.{0} Nat instLENat m n}, Eq.{1} (forall (a : Fin m), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLE m n h'))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (fun (_x : Fin m) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin m) => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin m) (Fin n)) (Fin m) (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin m) (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin m) (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast m n h))))
+Case conversion may be inaccurate. Consider using '#align fin.cast_le_of_eq Fin.castLE_of_eqₓ'. -/
+theorem castLE_of_eq {m n : ℕ} (h : m = n) {h' : m ≤ n} :
+    (castLE h' : Fin m → Fin n) = Fin.cast h :=
   funext fun _ => rfl
-#align fin.cast_le_of_eq Fin.castLe_of_eq
+#align fin.cast_le_of_eq Fin.castLE_of_eq
 
 #print Fin.cast_to_equiv /-
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
@@ -1697,7 +1697,7 @@ theorem cast_eq_cast (h : n = m) : (cast h : Fin n → Fin m) = cast (h ▸ rfl)
 #print Fin.castAdd /-
 /-- `cast_add m i` embeds `i : fin n` in `fin (n+m)`. See also `fin.nat_add` and `fin.add_nat`. -/
 def castAdd (m) : Fin n ↪o Fin (n + m) :=
-  castLe <| Nat.le_add_right n m
+  castLE <| Nat.le_add_right n m
 #align fin.cast_add Fin.castAdd
 -/
 
@@ -2100,7 +2100,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align fin.range_cast_succ Fin.range_castSuccₓ'. -/
 @[simp]
 theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) = { i | (i : ℕ) < n } :=
-  range_castLe _
+  range_castLE _
 #align fin.range_cast_succ Fin.range_castSucc
 
 /- warning: fin.coe_of_injective_cast_succ_symm -> Fin.coe_of_injective_castSucc_symm is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -1451,31 +1451,31 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
 #align fin.succ_succ_ne_one Fin.succ_succ_ne_one
 -/
 
-#print Fin.castLt /-
+#print Fin.castLT /-
 /-- `cast_lt i h` embeds `i` into a `fin` where `h` proves it belongs into.  -/
-def castLt (i : Fin m) (h : i.1 < n) : Fin n :=
+def castLT (i : Fin m) (h : i.1 < n) : Fin n :=
   ⟨i.1, h⟩
-#align fin.cast_lt Fin.castLt
+#align fin.cast_lt Fin.castLT
 -/
 
-#print Fin.coe_castLt /-
+#print Fin.coe_castLT /-
 @[simp]
-theorem coe_castLt (i : Fin m) (h : i.1 < n) : (castLt i h : ℕ) = i :=
+theorem coe_castLT (i : Fin m) (h : i.1 < n) : (castLT i h : ℕ) = i :=
   rfl
-#align fin.coe_cast_lt Fin.coe_castLt
+#align fin.coe_cast_lt Fin.coe_castLT
 -/
 
-#print Fin.castLt_mk /-
+#print Fin.castLT_mk /-
 @[simp]
-theorem castLt_mk (i n m : ℕ) (hn : i < n) (hm : i < m) : castLt ⟨i, hn⟩ hm = ⟨i, hm⟩ :=
+theorem castLT_mk (i n m : ℕ) (hn : i < n) (hm : i < m) : castLT ⟨i, hn⟩ hm = ⟨i, hm⟩ :=
   rfl
-#align fin.cast_lt_mk Fin.castLt_mk
+#align fin.cast_lt_mk Fin.castLT_mk
 -/
 
 #print Fin.castLe /-
 /-- `cast_le h i` embeds `i` into a larger `fin` type.  -/
 def castLe (h : n ≤ m) : Fin n ↪o Fin m :=
-  OrderEmbedding.ofStrictMono (fun a => castLt a (lt_of_lt_of_le a.2 h)) fun a b h => h
+  OrderEmbedding.ofStrictMono (fun a => castLT a (lt_of_lt_of_le a.2 h)) fun a b h => h
 #align fin.cast_le Fin.castLe
 -/
 
@@ -1744,27 +1744,27 @@ theorem castAdd_mk (m : ℕ) (i : ℕ) (h : i < n) : castAdd m ⟨i, h⟩ = ⟨i
   rfl
 #align fin.cast_add_mk Fin.castAdd_mk
 
-/- warning: fin.cast_add_cast_lt -> Fin.castAdd_castLt is a dubious translation:
+/- warning: fin.cast_add_cast_lt -> Fin.castAdd_castLT is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (hi : LT.lt.{0} Nat Nat.hasLt (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i hi)) i
+  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (hi : LT.lt.{0} Nat Nat.hasLt (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) i hi)) i
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (hi : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i) n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) i
-Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast_lt Fin.castAdd_castLtₓ'. -/
+  forall {n : Nat} (m : Nat) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (hi : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i) n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) i hi)) i
+Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast_lt Fin.castAdd_castLTₓ'. -/
 @[simp]
-theorem castAdd_castLt (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m (castLt i hi) = i :=
+theorem castAdd_castLT (m : ℕ) (i : Fin (n + m)) (hi : i.val < n) : castAdd m (castLT i hi) = i :=
   ext rfl
-#align fin.cast_add_cast_lt Fin.castAdd_castLt
+#align fin.cast_add_cast_lt Fin.castAdd_castLT
 
-/- warning: fin.cast_lt_cast_add -> Fin.castLt_castAdd is a dubious translation:
+/- warning: fin.cast_lt_cast_add -> Fin.castLT_castAdd is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i) (Fin.castAdd_lt n m i)) i
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) i) (Fin.castAdd_lt n m i)) i
 but is expected to have type
-  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) i) (Fin.castAdd_lt n m i)) i
-Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_add Fin.castLt_castAddₓ'. -/
+  forall {n : Nat} (m : Nat) (i : Fin n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) i) (Fin.castAdd_lt n m i)) i
+Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_add Fin.castLT_castAddₓ'. -/
 @[simp]
-theorem castLt_castAdd (m : ℕ) (i : Fin n) : castLt (castAdd m i) (castAdd_lt m i) = i :=
+theorem castLT_castAdd (m : ℕ) (i : Fin n) : castLT (castAdd m i) (castAdd_lt m i) = i :=
   ext rfl
-#align fin.cast_lt_cast_add Fin.castLt_castAdd
+#align fin.cast_lt_cast_add Fin.castLT_castAdd
 
 /- warning: fin.cast_add_cast -> Fin.castAdd_cast is a dubious translation:
 lean 3 declaration is
@@ -1926,27 +1926,27 @@ theorem succ_eq_last_succ {n : ℕ} (i : Fin n.succ) : i.succ = last (n + 1) ↔
 #align fin.succ_eq_last_succ Fin.succ_eq_last_succ
 -/
 
-/- warning: fin.cast_succ_cast_lt -> Fin.castSucc_cast_lt is a dubious translation:
+/- warning: fin.cast_succ_cast_lt -> Fin.castSucc_castLT is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i h)) i
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (HasLiftT.mk.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (CoeTCₓ.coe.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (coeBase.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat (Fin.coeToNat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) i) n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) i h)) i
 but is expected to have type
-  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) i
-Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_lt Fin.castSucc_cast_ltₓ'. -/
+  forall {n : Nat} (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (h : LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i h)) i
+Case conversion may be inaccurate. Consider using '#align fin.cast_succ_cast_lt Fin.castSucc_castLTₓ'. -/
 @[simp]
-theorem castSucc_cast_lt (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLt i h) = i :=
+theorem castSucc_castLT (i : Fin (n + 1)) (h : (i : ℕ) < n) : castSucc (castLT i h) = i :=
   Fin.eq_of_veq rfl
-#align fin.cast_succ_cast_lt Fin.castSucc_cast_lt
+#align fin.cast_succ_cast_lt Fin.castSucc_castLT
 
-/- warning: fin.cast_lt_cast_succ -> Fin.cast_lt_castSucc is a dubious translation:
+/- warning: fin.cast_lt_cast_succ -> Fin.castLT_castSucc is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) a) n), Eq.{1} (Fin n) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) h) a
+  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat Nat.hasLt ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) a) h) a
 but is expected to have type
-  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat instLTNat (Fin.val n a) n), Eq.{1} (Fin n) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) h) a
-Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_succ Fin.cast_lt_castSuccₓ'. -/
+  forall {n : Nat} (a : Fin n) (h : LT.lt.{0} Nat instLTNat (Fin.val n a) n), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) a) h) a
+Case conversion may be inaccurate. Consider using '#align fin.cast_lt_cast_succ Fin.castLT_castSuccₓ'. -/
 @[simp]
-theorem cast_lt_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLt (castSucc a) h = a := by
+theorem castLT_castSucc {n : ℕ} (a : Fin n) (h : (a : ℕ) < n) : castLT (castSucc a) h = a := by
   cases a <;> rfl
-#align fin.cast_lt_cast_succ Fin.cast_lt_castSucc
+#align fin.cast_lt_cast_succ Fin.castLT_castSucc
 
 /- warning: fin.cast_succ_lt_cast_succ_iff -> Fin.castSucc_lt_castSucc_iff is a dubious translation:
 lean 3 declaration is
@@ -2518,7 +2518,7 @@ theorem pred_one {n : ℕ} : Fin.pred (1 : Fin (n + 2)) (Ne.symm (ne_of_lt one_p
 
 #print Fin.pred_add_one /-
 theorem pred_add_one (i : Fin (n + 2)) (h : (i : ℕ) < n + 1) :
-    pred (i + 1) (ne_of_gt (add_one_pos _ (lt_iff_val_lt_val.mpr h))) = castLt i h :=
+    pred (i + 1) (ne_of_gt (add_one_pos _ (lt_iff_val_lt_val.mpr h))) = castLT i h :=
   by
   rw [ext_iff, coe_pred, coe_cast_lt, coe_add, coe_one, mod_eq_of_lt, add_tsub_cancel_right]
   exact add_lt_add_right h 1
@@ -2983,7 +2983,7 @@ Case conversion may be inaccurate. Consider using '#align fin.add_cases Fin.addC
 @[elab_as_elim]
 def addCases {m n : ℕ} {C : Fin (m + n) → Sort u} (hleft : ∀ i, C (castAdd n i))
     (hright : ∀ i, C (natAdd m i)) (i : Fin (m + n)) : C i :=
-  if hi : (i : ℕ) < m then Eq.recOn (castAdd_castLt n i hi) (hleft (castLt i hi))
+  if hi : (i : ℕ) < m then Eq.recOn (castAdd_castLT n i hi) (hleft (castLT i hi))
   else Eq.recOn (natAdd_subNat_cast (le_of_not_lt hi)) (hright _)
 #align fin.add_cases Fin.addCases
 
@@ -3470,19 +3470,19 @@ theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 <
   · simp [succ_above_above _ _ (le_of_not_lt H)]
 #align fin.succ_above_pos Fin.succAbove_pos
 
-/- warning: fin.succ_above_cast_lt -> Fin.succAbove_castLt is a dubious translation:
+/- warning: fin.succ_above_cast_lt -> Fin.succAbove_castLT is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hx : optParam.{0} (LT.lt.{0} Nat (Preorder.toLT.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) y) n h (Fin.le_last n y))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x hx)) x
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) x y) (hx : optParam.{0} (LT.lt.{0} Nat (Preorder.toLT.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) y) n h (Fin.le_last n y))), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) x hx)) x
 but is expected to have type
-  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hx : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n h (Fin.le_last n y))), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) x
-Case conversion may be inaccurate. Consider using '#align fin.succ_above_cast_lt Fin.succAbove_castLtₓ'. -/
+  forall {n : Nat} {x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x y) (hx : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n h (Fin.le_last n y))), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x hx)) x
+Case conversion may be inaccurate. Consider using '#align fin.succ_above_cast_lt Fin.succAbove_castLTₓ'. -/
 @[simp]
-theorem succAbove_castLt {x y : Fin (n + 1)} (h : x < y)
-    (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLt hx) = x :=
+theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
+    (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLT hx) = x :=
   by
   rw [succ_above_below, cast_succ_cast_lt]
   exact h
-#align fin.succ_above_cast_lt Fin.succAbove_castLt
+#align fin.succ_above_cast_lt Fin.succAbove_castLT
 
 /- warning: fin.succ_above_pred -> Fin.succAbove_pred is a dubious translation:
 lean 3 declaration is
@@ -3498,16 +3498,16 @@ theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y) (hy : y ≠ 0 := (x.zero_
   simpa [le_iff_coe_le_coe] using Nat.le_pred_of_lt h
 #align fin.succ_above_pred Fin.succAbove_pred
 
-/- warning: fin.cast_lt_succ_above -> Fin.castLt_succAbove is a dubious translation:
+/- warning: fin.cast_lt_succ_above -> Fin.castLT_succAbove is a dubious translation:
 lean 3 declaration is
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(OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.partialOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (Fin.succAbove n y) x) h') x
 but is expected to have type
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1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) x) y) (h' : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x)) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n (Iff.mpr (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x) y) (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) x) y) (Fin.succAbove_lt_iff n y x) h) (Fin.le_last n y))), Eq.{1} (Fin n) (Fin.castLt n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x) h') x
-Case conversion may be inaccurate. Consider using '#align fin.cast_lt_succ_above Fin.castLt_succAboveₓ'. -/
-theorem castLt_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
+  forall {n : Nat} {x : Fin n} {y : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))} (h : LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) x) y) (h' : optParam.{0} (LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x)) n) (lt_of_lt_of_le.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x)) (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) y) n (Iff.mpr (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x) y) (LT.lt.{0} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) x) y) (Fin.succAbove_lt_iff n y x) h) (Fin.le_last n y))), Eq.{1} (Fin n) (Fin.castLT n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.succAbove n y)) x) h') x
+Case conversion may be inaccurate. Consider using '#align fin.cast_lt_succ_above Fin.castLT_succAboveₓ'. -/
+theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
     (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
-    (y.succAbove x).castLt h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
-#align fin.cast_lt_succ_above Fin.castLt_succAbove
+    (y.succAbove x).castLT h' = x := by simp only [succ_above_below _ _ h, cast_lt_cast_succ]
+#align fin.cast_lt_succ_above Fin.castLT_succAbove
 
 /- warning: fin.pred_succ_above -> Fin.pred_succAbove is a dubious translation:
 lean 3 declaration is
@@ -3722,7 +3722,7 @@ section PredAbove
 /-- `pred_above p i` embeds `i : fin (n+1)` into `fin n` by subtracting one if `p < i`. -/
 def predAbove (p : Fin n) (i : Fin (n + 1)) : Fin n :=
   if h : p.cast_succ < i then i.pred (ne_of_lt (lt_of_le_of_lt (zero_le p.cast_succ) h)).symm
-  else i.castLt (lt_of_le_of_lt (le_of_not_lt h) p.2)
+  else i.castLT (lt_of_le_of_lt (le_of_not_lt h) p.2)
 #align fin.pred_above Fin.predAbove
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -1683,7 +1683,7 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (Fin.cast n m h)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h)) (cast.{1} (Fin n) (Fin m) (Eq.subst.{1} Nat (fun (_x : Nat) => Eq.{2} Type (Fin n) (Fin _x)) n m h (rfl.{2} Type (Fin n))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8122 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8123 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8122) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8122) (rfl.{1} Nat n) m h)))))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8323 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8324 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8323) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8323) (rfl.{1} Nat n) m h)))))
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
@@ -1770,7 +1770,7 @@ theorem castLt_castAdd (m : ℕ) (i : Fin n) : castLt (castAdd m i) (castAdd_lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') 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Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8627 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8627 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2196,7 +2196,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') 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Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.10336 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10336 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2719,7 +2719,7 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.induction.{u1} n C h0 hs (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13129 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13129) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13330 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13330) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
 Case conversion may be inaccurate. Consider using '#align fin.induction_zero Fin.induction_zeroₓ'. -/
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2731,7 +2731,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) (Fin.induction.{u1} n C h0 hs (Fin.succ n i)) (hs i (Fin.induction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13321 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13321) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13522 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13522) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -3027,7 +3027,7 @@ end Rec
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α α (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) r f f) (forall (i : Fin n), r (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15161 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15163 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15161 x._@.Mathlib.Data.Fin.Basic._hyg.15163) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15362 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15364 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15362 x._@.Mathlib.Data.Fin.Basic._hyg.15364) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

@@ -1683,7 +1683,7 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (Fin.cast n m h)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h)) (cast.{1} (Fin n) (Fin m) (Eq.subst.{1} Nat (fun (_x : Nat) => Eq.{2} Type (Fin n) (Fin _x)) n m h (rfl.{2} Type (Fin n))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8105 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8106 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8105) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8105) (rfl.{1} Nat n) m h)))))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8122 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8123 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8122) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8122) (rfl.{1} Nat n) m h)))))
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
@@ -1770,7 +1770,7 @@ theorem castLt_castAdd (m : ℕ) (i : Fin n) : castLt (castAdd m i) (castAdd_lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n' m)) i))
+  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8426 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8426 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2196,7 +2196,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i))
+  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.10135 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10135 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2719,7 +2719,7 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.induction.{u1} n C h0 hs (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13112 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13112) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13129 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13129) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
 Case conversion may be inaccurate. Consider using '#align fin.induction_zero Fin.induction_zeroₓ'. -/
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2731,7 +2731,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) (Fin.induction.{u1} n C h0 hs (Fin.succ n i)) (hs i (Fin.induction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13304 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13304) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13321 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13321) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -3027,7 +3027,7 @@ end Rec
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α α (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) r f f) (forall (i : Fin n), r (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15144 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15146 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15144 x._@.Mathlib.Data.Fin.Basic._hyg.15146) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15161 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15163 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15161 x._@.Mathlib.Data.Fin.Basic._hyg.15163) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -1683,7 +1683,7 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (Fin.cast n m h)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h)) (cast.{1} (Fin n) (Fin m) (Eq.subst.{1} Nat (fun (_x : Nat) => Eq.{2} Type (Fin n) (Fin _x)) n m h (rfl.{2} Type (Fin n))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8036 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8037 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8036) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8036) (rfl.{1} Nat n) m h)))))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8105 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8106 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8105) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8105) (rfl.{1} Nat n) m h)))))
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
@@ -1770,7 +1770,7 @@ theorem castLt_castAdd (m : ℕ) (i : Fin n) : castLt (castAdd m i) (castAdd_lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n' m)) i))
+  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8409 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8409 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2196,7 +2196,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i))
+  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (fun (_x : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.10118 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10118 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2719,7 +2719,7 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.induction.{u1} n C h0 hs (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13043 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13043) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13112 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13112) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
 Case conversion may be inaccurate. Consider using '#align fin.induction_zero Fin.induction_zeroₓ'. -/
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2731,7 +2731,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) (Fin.induction.{u1} n C h0 hs (Fin.succ n i)) (hs i (Fin.induction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13235 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13235) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13304 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13304) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -3027,7 +3027,7 @@ end Rec
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α α (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) r f f) (forall (i : Fin n), r (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15075 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15077 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15075 x._@.Mathlib.Data.Fin.Basic._hyg.15077) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15144 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15146 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15144 x._@.Mathlib.Data.Fin.Basic._hyg.15146) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -603,7 +603,7 @@ def rev : Equiv.Perm (Fin n) :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.Perm.{1} (Fin n)) (fun (_x : Equiv.{1, 1} (Fin n) (Fin n)) => (Fin n) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+  forall {n : Nat} (i : Fin n), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Fin.val n i) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
 Case conversion may be inaccurate. Consider using '#align fin.coe_rev Fin.val_revₓ'. -/
 @[simp]
 theorem val_rev (i : Fin n) : (i.rev : ℕ) = n - (i + 1) :=
@@ -695,7 +695,7 @@ def revOrderIso {n} : (Fin n)ᵒᵈ ≃o Fin n :=
 lean 3 declaration is
   forall {n : Nat} (i : Fin n), Eq.{1} (OrderDual.{0} (Fin n)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (Fin.hasLe n) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n))) (fun (_x : RelIso.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)))) => (Fin n) -> (OrderDual.{0} (Fin n))) (RelIso.hasCoeToFun.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)))) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.hasLe.{0} (Fin n) (Fin.hasLe n)) (Fin.hasLe n) (Fin.revOrderIso n)) i) (coeFn.{1, 1} (Equiv.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (fun (_x : Equiv.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) => (Fin n) -> (OrderDual.{0} (Fin n))) (Equiv.hasCoeToFun.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (OrderDual.toDual.{0} (Fin n)) (coeFn.{1, 1} (Equiv.Perm.{1} (Fin n)) (fun (_x : Equiv.{1, 1} (Fin n) (Fin n)) => (Fin n) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
 but is expected to have type
-  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => OrderDual.{0} (Fin n)) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => OrderDual.{0} (Fin n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (Fin n) (OrderDual.{0} (Fin n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) (instLEFin n) (Fin.revOrderIso n)))) i) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i))) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i) (fun (_x : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i) => OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i)) _x) (Equiv.instFunLikeEquiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i))) (OrderDual.toDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) i)) (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
+  forall {n : Nat} (i : Fin n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => OrderDual.{0} (Fin n)) i) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => OrderDual.{0} (Fin n)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n))) (Fin n) (OrderDual.{0} (Fin n)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (OrderDual.{0} (Fin n)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (OrderDual.{0} (Fin n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : OrderDual.{0} (Fin n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : OrderDual.{0} (Fin n)) => LE.le.{0} (OrderDual.{0} (Fin n)) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{0, 0} (OrderDual.{0} (Fin n)) (Fin n) (OrderDual.instLEOrderDual.{0} (Fin n) (instLEFin n)) (instLEFin n) (Fin.revOrderIso n)))) i) (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (fun (_x : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) => OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) _x) (Equiv.instFunLikeEquiv.{1, 1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i) (OrderDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i))) (OrderDual.toDual.{0} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) i)) (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin n)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Fin n) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin n) (Fin n)) (Fin.rev n) i))
 Case conversion may be inaccurate. Consider using '#align fin.rev_order_iso_symm_apply Fin.revOrderIso_symm_applyₓ'. -/
 @[simp]
 theorem revOrderIso_symm_apply (i : Fin n) : revOrderIso.symm i = OrderDual.toDual i.rev :=
@@ -1527,7 +1527,7 @@ theorem range_castLe {n k : ℕ} (h : n ≤ k) : Set.range (castLe h) = { i | (i
 lean 3 declaration is
   forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat Nat.hasLe n k) (i : Fin k) (hi : Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))), Eq.{1} Nat ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) (coeFn.{1, 1} (Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Fin n)) => (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) -> (Fin n)) (Equiv.hasCoeToFun.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (coeSort.{1, 2} (Set.{0} (Fin k)) Type (Set.hasCoeToSort.{0} (Fin k)) (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k)) (Fin.castLe n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.Mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.hasMem.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (coeFn.{1, 1} (RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) => (Fin n) -> (Fin k)) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin k) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin k) (Fin.hasLe k))) (Fin.castLe n k h)))) i hi))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin k) Nat (HasLiftT.mk.{1, 1} (Fin k) Nat (CoeTCₓ.coe.{1, 1} (Fin k) Nat (coeBase.{1, 1} (Fin k) Nat (Fin.coeToNat k)))) i)
 but is expected to have type
-  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k) (i : Fin k) (hi : Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Fin n)) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (fun (_x : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) i hi))) (Fin.val k i)
+  forall {n : Nat} {k : Nat} (h : LE.le.{0} Nat instLENat n k) (i : Fin k) (hi : Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) i (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))), Eq.{1} Nat (Fin.val n (FunLike.coe.{1, 1, 1} (Equiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Fin n)) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (fun (_x : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) => Fin n) _x) (Equiv.instFunLikeEquiv.{1, 1} (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Fin n)) (Equiv.symm.{1, 1} (Fin n) (Set.Elem.{0} (Fin k) (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) (Equiv.ofInjective.{1, 0} (Fin n) (Fin k) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))) (RelEmbedding.injective.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h)))) (Subtype.mk.{1} (Fin k) (fun (x : Fin k) => Membership.mem.{0, 0} (Fin k) (Set.{0} (Fin k)) (Set.instMembershipSet.{0} (Fin k)) x (Set.range.{0, 1} (Fin k) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin k) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin k)) (Fin n) (Fin k) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin k))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin k) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin k) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin k) => LE.le.{0} (Fin k) (instLEFin k) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castLe n k h))))) i hi))) (Fin.val k i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_le_symm Fin.coe_of_injective_castLe_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castLe_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (hi) :
@@ -1683,7 +1683,7 @@ theorem cast_to_equiv (h : n = m) : (cast h).toEquiv = Equiv.cast (h ▸ rfl) :=
 lean 3 declaration is
   forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} ((fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (Fin.cast n m h)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n) (Fin m) (Fin.hasLe n) (Fin.hasLe m)) (fun (_x : RelIso.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) => (Fin n) -> (Fin m)) (RelIso.hasCoeToFun.{0, 0} (Fin n) (Fin m) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin m) (Fin.hasLe m))) (Fin.cast n m h)) (cast.{1} (Fin n) (Fin m) (Eq.subst.{1} Nat (fun (_x : Nat) => Eq.{2} Type (Fin n) (Fin _x)) n m h (rfl.{2} Type (Fin n))))
 but is expected to have type
-  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.7988 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.7989 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.7988) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.7988) (rfl.{1} Nat n) m h)))))
+  forall {n : Nat} {m : Nat} (h : Eq.{1} Nat n m), Eq.{1} (forall (a : Fin n), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (fun (a : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin m) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin m)) (Fin n) (Fin m) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin m))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n) (Fin m) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin m) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin m) => LE.le.{0} (Fin m) (instLEFin m) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n m (Eq.rec.{0, 1} Nat n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8036 : Nat) (h._@.Mathlib.Data.Fin.Basic._hyg.8037 : Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8036) => Eq.{1} Nat n x._@.Mathlib.Data.Fin.Basic._hyg.8036) (rfl.{1} Nat n) m h)))))
 Case conversion may be inaccurate. Consider using '#align fin.cast_eq_cast Fin.cast_eq_castₓ'. -/
 /-- While in many cases `fin.cast` is better than `equiv.cast`/`cast`, sometimes we want to apply
 a generic theorem about `cast`. -/
@@ -1770,7 +1770,7 @@ theorem castLt_castAdd (m : ℕ) (i : Fin n) : castLt (castAdd m i) (castAdd_lt
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.castAdd n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.castAdd n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} (m : Nat) (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8283 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8283 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8283 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8283 m) n))) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8283 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8283 m) n')) (fun (_x : Fin ((fun 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(x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.8340 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.8340 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castAdd n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.cast_add_cast Fin.castAdd_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_cast_add_left`. -/
 theorem castAdd_cast {n n' : ℕ} (m : ℕ) (i : Fin n') (h : n' = n) :
@@ -2107,7 +2107,7 @@ theorem range_castSucc {n : ℕ} : Set.range (castSucc : Fin n → Fin n.succ) =
 lean 3 declaration is
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n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n)))) (Fin n)) (fun (_x : Equiv.{1, 1} (coeSort.{1, 2} (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n))) (Fin.castSucc_injective n))) (Subtype.mk.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Membership.mem.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Set.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Set.instMembershipSet.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) x (Set.range.{0, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin n) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n))))) i hi))) (Fin.val (Nat.succ n) i)
 Case conversion may be inaccurate. Consider using '#align fin.coe_of_injective_cast_succ_symm Fin.coe_of_injective_castSucc_symmₓ'. -/
 @[simp]
 theorem coe_of_injective_castSucc_symm {n : ℕ} (i : Fin (n + 1)) (hi) :
@@ -2196,7 +2196,7 @@ theorem cast_addNat_zero {n n' : ℕ} (i : Fin n) (h : n + 0 = n') :
 lean 3 declaration is
   forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.addNat n m) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin n') (Fin n) (Fin.hasLe n') (Fin.hasLe n)) (fun (_x : RelIso.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) => (Fin n') -> (Fin n)) (RelIso.hasCoeToFun.{0, 0} (Fin n') (Fin n) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin n) (Fin.hasLe n))) (Fin.cast n' n h) i)) (coeFn.{1, 1} (OrderIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (fun (_x : RelIso.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m))) (RelIso.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m)))) (Fin.cast (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n m) (congr_arg.{1, 1} Nat Nat n' n (fun {n' : Nat} => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m) h)) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe n') (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (fun (_x : RelEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) => (Fin n') -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (LE.le.{0} (Fin n') (Fin.hasLe n')) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n' m)))) (Fin.addNat n' m) i))
 but is expected to have type
-  forall {n : Nat} {n' : Nat} {m : Nat} (i : Fin n') (h : Eq.{1} Nat n' n), Eq.{1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (a : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) a) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast n' n h))) i)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n m)) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin n) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin n)) (Fin n') (Fin n) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin n))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin n') (Fin n) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin n') 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Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{0, 0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n')) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (n' : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) => LE.le.{0} (Fin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) (instLEFin ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n)) n' x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Fin.cast ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n') ((fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) n) (congr_arg.{1, 1} Nat Nat n' n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.10049 : Nat) => HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) x._@.Mathlib.Data.Fin.Basic._hyg.10049 m) h)))) (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (fun (_x : Fin n') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n') => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m))) (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)))) (RelEmbedding.toEmbedding.{0, 0} (Fin n') (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n') (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n') => LE.le.{0} (Fin n') (instLEFin n') x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n' m)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.addNat n' m)) i))
 Case conversion may be inaccurate. Consider using '#align fin.add_nat_cast Fin.addNat_castₓ'. -/
 /-- For rewriting in the reverse direction, see `fin.cast_add_nat_left`. -/
 theorem addNat_cast {n n' m : ℕ} (i : Fin n') (h : n' = n) :
@@ -2719,7 +2719,7 @@ def induction {C : Fin (n + 1) → Sort _} (h0 : C 0) (hs : ∀ i : Fin n, C i.c
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Fin.induction.{u1} n C h0 hs (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) h0
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.12867 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.12867) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))), Eq.{u1} (C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13043 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13043) h0 hs i) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) h0
 Case conversion may be inaccurate. Consider using '#align fin.induction_zero Fin.induction_zeroₓ'. -/
 @[simp]
 theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -2731,7 +2731,7 @@ theorem induction_zero {C : Fin (n + 1) → Sort _} (h0 : C 0)
 lean 3 declaration is
   forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (hs : forall (i : Fin n), (C (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) (Fin.induction.{u1} n C h0 hs (Fin.succ n i)) (hs i (Fin.induction.{u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => C _x) h0 hs (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)))
 but is expected to have type
-  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13053 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13053) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
+  forall {n : Nat} {C : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> Sort.{u1}} (h0 : C (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (hs : forall (i : Fin n), (C (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) -> (C (Fin.succ n i))) (i : Fin n), Eq.{u1} (C (Fin.succ n i)) ((fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.induction.{u1} n (fun (x._@.Mathlib.Data.Fin.Basic._hyg.13235 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => C x._@.Mathlib.Data.Fin.Basic._hyg.13235) h0 hs i) (Fin.succ n i)) (hs i (Fin.induction.{u1} n C h0 hs (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)))
 Case conversion may be inaccurate. Consider using '#align fin.induction_succ Fin.induction_succₓ'. -/
 @[simp]
 theorem induction_succ {C : Fin (n + 1) → Sort _} (h0 : C 0)
@@ -3027,7 +3027,7 @@ end Rec
 lean 3 declaration is
   forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) α α (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) r f f) (forall (i : Fin n), r (f (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i)) (f (Fin.succ n i)))
 but is expected to have type
-  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.14871 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.14873 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.14871 x._@.Mathlib.Data.Fin.Basic._hyg.14873) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
+  forall {n : Nat} {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsTrans.{u1} α r] {f : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> α}, Iff (Relator.LiftFun.{1, 1, succ u1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) α α (fun (x._@.Mathlib.Data.Fin.Basic._hyg.15075 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Data.Fin.Basic._hyg.15077 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Data.Fin.Basic._hyg.15075 x._@.Mathlib.Data.Fin.Basic._hyg.15077) r f f) (forall (i : Fin n), r (f (FunLike.coe.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (EmbeddingLike.toFunLike.{1, 1, 1} (Function.Embedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Function.instEmbeddingLikeEmbedding.{1, 1} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.toEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Fin.castSucc n)) i)) (f (Fin.succ n i)))
 Case conversion may be inaccurate. Consider using '#align fin.lift_fun_iff_succ Fin.lift_fun_iff_succₓ'. -/
 theorem lift_fun_iff_succ {α : Type _} (r : α → α → Prop) [IsTrans α r] {f : Fin (n + 1) → α} :
     ((· < ·) ⇒ r) f f ↔ ∀ i : Fin n, r (f i.cast_succ) (f i.succ) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

A PR accompanying #12339.

Zulip discussion

@@ -1592,8 +1592,8 @@ theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a
 @[simp]
 theorem lt_sub_one_iff {n : ℕ} {k : Fin (n + 2)} : k < k - 1 ↔ k = 0 := by
   rcases k with ⟨_ | k, hk⟩
-  simp only [zero_eq, zero_eta, zero_sub, lt_iff_val_lt_val, val_zero, coe_neg_one, add_pos_iff,
-    _root_.zero_lt_one, or_true]
+  · simp only [zero_eq, zero_eta, zero_sub, lt_iff_val_lt_val, val_zero, coe_neg_one, add_pos_iff,
+      _root_.zero_lt_one, or_true]
   have : (k + 1 + (n + 1)) % (n + 2) = k % (n + 2) := by
     rw [add_right_comm, add_assoc, add_mod_right]
   simp [lt_iff_val_lt_val, ext_iff, Fin.coe_sub, succ_eq_add_one, this,

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -662,7 +662,7 @@ theorem ofNat''_eq_cast (n : ℕ) [NeZero n] (a : ℕ) : (Fin.ofNat'' a : Fin n)
   rfl
 #align fin.of_nat_eq_coe Fin.ofNat''_eq_cast
 
-@[simp] lemma val_nat_cast (a n : ℕ) [NeZero n] : (a : Fin n).val = a % n := rfl
+@[simp] lemma val_natCast (a n : ℕ) [NeZero n] : (a : Fin n).val = a % n := rfl
 
 -- Porting note: is this the right name for things involving `Nat.cast`?
 /-- Converting an in-range number to `Fin (n + 1)` produces a result
@@ -683,9 +683,9 @@ in the same value.  -/
 -- Porting note: this is syntactically the same as `cast_val_of_lt`
 #align fin.coe_coe_eq_self Fin.cast_val_eq_self
 
-@[simp] lemma nat_cast_self (n : ℕ) [NeZero n] : (n : Fin n) = 0 := by ext; simp
+@[simp] lemma natCast_self (n : ℕ) [NeZero n] : (n : Fin n) = 0 := by ext; simp
 
-@[simp] lemma nat_cast_eq_zero {a n : ℕ} [NeZero n] : (a : Fin n) = 0 ↔ n ∣ a := by
+@[simp] lemma natCast_eq_zero {a n : ℕ} [NeZero n] : (a : Fin n) = 0 ↔ n ∣ a := by
   simp [ext_iff, Nat.dvd_iff_mod_eq_zero]
 
 @[simp]
@@ -705,7 +705,7 @@ end OfNatCoe
 
 @[simp]
 theorem one_eq_zero_iff [NeZero n] : (1 : Fin n) = 0 ↔ n = 1 := by
-  rw [← Nat.cast_one, nat_cast_eq_zero, Nat.dvd_one]
+  rw [← Nat.cast_one, natCast_eq_zero, Nat.dvd_one]
 #align fin.one_eq_zero_iff Fin.one_eq_zero_iff
 
 @[simp]
@@ -1653,7 +1653,7 @@ theorem exists_eq_add_of_lt {n : ℕ} {a b : Fin (n + 1)} (h : a < b) :
 @[simp]
 theorem neg_last (n : ℕ) : -Fin.last n = 1 := by simp [neg_eq_iff_add_eq_zero]
 
-theorem neg_nat_cast_eq_one (n : ℕ) : -(n : Fin (n + 1)) = 1 := by
+theorem neg_natCast_eq_one (n : ℕ) : -(n : Fin (n + 1)) = 1 := by
   simp only [cast_nat_eq_last, neg_last]
 
 lemma pos_of_ne_zero {n : ℕ} {a : Fin (n + 1)} (h : a ≠ 0) :

The @[simp] annotation is not used in mathlib, and triggered a linter failure that I don't care to investigate unnecessarily.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -1609,7 +1609,6 @@ theorem le_sub_one_iff {n : ℕ} {k : Fin (n + 1)} : k ≤ k - 1 ↔ k = 0 := by
   simp
 #align fin.le_sub_one_iff Fin.le_sub_one_iff
 
-@[simp]
 theorem sub_one_lt_iff {n : ℕ} {k : Fin (n + 1)} : k - 1 < k ↔ 0 < k :=
   not_iff_not.1 <| by simp only [not_lt, le_sub_one_iff, le_zero_iff]
 #align fin.sub_one_lt_iff Fin.sub_one_lt_iff

and reduce its scope in a few other instances. Mostly in CategoryTheory and Data this time; some Combinatorics also.

Co-authored-by: Richard Osborn <richardosborn@mac.com>

@@ -72,8 +72,6 @@ This file expands on the development in the core library.
 
 -/
 
-set_option autoImplicit true
-
 universe u v
 
 open Fin Nat Function
@@ -85,7 +83,7 @@ def finZeroElim {α : Fin 0 → Sort*} (x : Fin 0) : α x :=
 
 namespace Fin
 
-instance : CanLift ℕ (Fin n) Fin.val (· < n) where
+instance {n : ℕ} : CanLift ℕ (Fin n) Fin.val (· < n) where
   prf k hk := ⟨⟨k, hk⟩, rfl⟩
 
 /-- A dependent variant of `Fin.elim0`. -/
@@ -554,7 +552,7 @@ protected theorem zero_add [NeZero n] (k : Fin n) : 0 + k = k := by
   simp [ext_iff, add_def, mod_eq_of_lt (is_lt k)]
 #align fin.zero_add Fin.zero_add
 
-instance [NeZero n] : OfNat (Fin n) a where
+instance {a : ℕ} [NeZero n] : OfNat (Fin n) a where
   ofNat := Fin.ofNat' a (NeZero.pos n)
 
 instance inhabited (n : ℕ) [NeZero n] : Inhabited (Fin n) :=
@@ -571,8 +569,8 @@ theorem default_eq_zero (n : ℕ) [NeZero n] : (default : Fin n) = 0 :=
 
 section from_ad_hoc
 
-@[simp] lemma ofNat'_zero [NeZero n] : (Fin.ofNat' 0 h : Fin n) = 0 := rfl
-@[simp] lemma ofNat'_one [NeZero n] : (Fin.ofNat' 1 h : Fin n) = 1 := rfl
+@[simp] lemma ofNat'_zero {h : 0 < n} [NeZero n] : (Fin.ofNat' 0 h : Fin n) = 0 := rfl
+@[simp] lemma ofNat'_one {h : 0 < n} [NeZero n] : (Fin.ofNat' 1 h : Fin n) = 1 := rfl
 
 end from_ad_hoc
 
@@ -987,12 +985,12 @@ def castSuccEmb : Fin n ↪o Fin (n + 1) :=
 #align fin.cast_succ_lt_cast_succ_iff Fin.castSucc_lt_castSucc_iff
 
 @[simp]
-theorem castSucc_le_castSucc_iff : castSucc a ≤ castSucc b ↔ a ≤ b := Iff.rfl
+theorem castSucc_le_castSucc_iff {a b : Fin n} : castSucc a ≤ castSucc b ↔ a ≤ b := Iff.rfl
 @[simp]
-theorem succ_le_castSucc_iff : succ a ≤ castSucc b ↔ a < b := by
+theorem succ_le_castSucc_iff {a b : Fin n} : succ a ≤ castSucc b ↔ a < b := by
   rw [le_castSucc_iff, succ_lt_succ_iff]
 @[simp]
-theorem castSucc_lt_succ_iff : castSucc a < succ b ↔ a ≤ b := by
+theorem castSucc_lt_succ_iff {a b : Fin n} : castSucc a < succ b ↔ a ≤ b := by
   rw [castSucc_lt_iff_succ_le, succ_le_succ_iff]
 
 theorem le_of_castSucc_lt_of_succ_lt {a b : Fin (n + 1)} {i : Fin n}
@@ -1194,11 +1192,11 @@ section Pred
 #align fin.add_nat_sub_nat Fin.addNat_subNat
 #align fin.sub_nat_add_nat Fin.subNat_addNat
 
-theorem strictMono_pred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ 0)
+theorem strictMono_pred_comp {α : Type*} [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ 0)
     (hf₂ : StrictMono f) : StrictMono (fun a => pred (f a) (hf a)) :=
     fun _ _ h => pred_lt_pred_iff.2 (hf₂ h)
 
-theorem monotone_pred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ 0)
+theorem monotone_pred_comp {α : Type*} [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ 0)
     (hf₂ : Monotone f) : Monotone (fun a => pred (f a) (hf a)) :=
     fun _ _ h => pred_le_pred_iff.2 (hf₂ h)
 
@@ -1211,13 +1209,13 @@ theorem pred_one' [NeZero n] (h := (zero_ne_one' (n := n)).symm) :
 theorem pred_last (h := last_pos'.ne') :
     pred (last (n + 1)) h = last n := by simp_rw [← succ_last, pred_succ]
 
-theorem pred_lt_iff {i : Fin (n + 1)} (hi : i ≠ 0) : pred i hi < j ↔ i < succ j := by
+theorem pred_lt_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ 0) : pred i hi < j ↔ i < succ j := by
   rw [← succ_lt_succ_iff, succ_pred]
-theorem lt_pred_iff {i : Fin (n + 1)} (hi : i ≠ 0) : j < pred i hi ↔ succ j < i := by
+theorem lt_pred_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ 0) : j < pred i hi ↔ succ j < i := by
   rw [← succ_lt_succ_iff, succ_pred]
-theorem pred_le_iff {i : Fin (n + 1)} (hi : i ≠ 0) : pred i hi ≤ j ↔ i ≤ succ j := by
+theorem pred_le_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ 0) : pred i hi ≤ j ↔ i ≤ succ j := by
   rw [← succ_le_succ_iff, succ_pred]
-theorem le_pred_iff {i : Fin (n + 1)} (hi : i ≠ 0) : j ≤ pred i hi ↔ succ j ≤ i := by
+theorem le_pred_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ 0) : j ≤ pred i hi ↔ succ j ≤ i := by
   rw [← succ_le_succ_iff, succ_pred]
 
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
@@ -1297,27 +1295,27 @@ theorem castPred_le_castPred_iff {i j : Fin (n + 1)} {hi : i ≠ last n} {hj : j
 theorem castPred_lt_castPred_iff {i j : Fin (n + 1)} {hi : i ≠ last n} {hj : j ≠ last n} :
     castPred i hi < castPred j hj ↔ i < j := Iff.rfl
 
-theorem strictMono_castPred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ last n)
-    (hf₂ : StrictMono f) : StrictMono (fun a => castPred (f a) (hf a)) :=
+theorem strictMono_castPred_comp {α : Type*} [Preorder α] {f : α → Fin (n + 1)}
+    (hf : ∀ a, f a ≠ last n) (hf₂ : StrictMono f) : StrictMono (fun a => castPred (f a) (hf a)) :=
     fun _ _ h => castPred_lt_castPred_iff.2 (hf₂ h)
 
-theorem monotone_castPred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ last n)
-    (hf₂ : Monotone f) : Monotone (fun a => castPred (f a) (hf a)) :=
+theorem monotone_castPred_comp {α : Type*} [Preorder α] {f : α → Fin (n + 1)}
+    (hf : ∀ a, f a ≠ last n) (hf₂ : Monotone f) : Monotone (fun a => castPred (f a) (hf a)) :=
     fun _ _ h => castPred_le_castPred_iff.2 (hf₂ h)
 
-theorem castPred_lt_iff {i : Fin (n + 1)} (hi : i ≠ last n) :
+theorem castPred_lt_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ last n) :
     castPred i hi < j ↔ i < castSucc j := by
   rw [← castSucc_lt_castSucc_iff, castSucc_castPred]
 
-theorem lt_castPred_iff {i : Fin (n + 1)} (hi : i ≠ last n) :
+theorem lt_castPred_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ last n) :
     j < castPred i hi ↔ castSucc j < i := by
   rw [← castSucc_lt_castSucc_iff, castSucc_castPred]
 
-theorem castPred_le_iff {i : Fin (n + 1)} (hi : i ≠ last n) :
+theorem castPred_le_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ last n) :
     castPred i hi ≤ j ↔ i ≤ castSucc j := by
   rw [← castSucc_le_castSucc_iff, castSucc_castPred]
 
-theorem le_castPred_iff {i : Fin (n + 1)} (hi : i ≠ last n) :
+theorem le_castPred_iff {j : Fin n} {i : Fin (n + 1)} (hi : i ≠ last n) :
     j ≤ castPred i hi ↔ castSucc j ≤ i := by
   rw [← castSucc_le_castSucc_iff, castSucc_castPred]
 
@@ -1339,11 +1337,12 @@ theorem castPred_one [NeZero n] (h := one_lt_last.ne) : castPred (1 : Fin (n + 2
   · rfl
 #align fin.cast_pred_one Fin.castPred_one
 
-theorem rev_pred (h : i ≠ 0) (h' := rev_ne_iff.mpr ((rev_last _).symm ▸ h)) :
+theorem rev_pred {i : Fin (n + 1)} (h : i ≠ 0) (h' := rev_ne_iff.mpr ((rev_last _).symm ▸ h)) :
     rev (pred i h) = castPred (rev i) h' := by
   rw [← castSucc_inj, castSucc_castPred, ← rev_succ, succ_pred]
 
-theorem rev_castPred (h : i ≠ last n) (h' := rev_ne_iff.mpr ((rev_zero _).symm ▸ h)) :
+theorem rev_castPred {i : Fin (n + 1)}
+    (h : i ≠ last n) (h' := rev_ne_iff.mpr ((rev_zero _).symm ▸ h)) :
     rev (castPred i h) = pred (rev i) h' := by
   rw [← succ_inj, succ_pred, ← rev_castSucc, castSucc_castPred]
 
@@ -1387,7 +1386,8 @@ theorem pred_lt_castPred_iff {a b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ last
     pred a ha < castPred b hb ↔ a ≤ b := by
   rw [lt_castPred_iff, castSucc_pred_lt_iff ha]
 
-theorem pred_lt_castPred (h₁ : a ≠ 0) (h₂ : a ≠ last n) : pred a h₁ < castPred a h₂ := by
+theorem pred_lt_castPred {a : Fin (n + 1)} (h₁ : a ≠ 0) (h₂ : a ≠ last n) :
+    pred a h₁ < castPred a h₂ := by
   rw [pred_lt_castPred_iff]
 
 end CastPred

@@ -1088,7 +1088,7 @@ theorem coe_eq_castSucc {a : Fin n} : (a : Fin (n + 1)) = castSucc a := by
 #align fin.coe_eq_cast_succ Fin.coe_eq_castSucc
 
 theorem coe_succ_lt_iff_lt {n : ℕ} {j k : Fin n} : (j : Fin <| n + 1) < k ↔ j < k := by
-  simp only [coe_eq_castSucc]; rfl
+  simp only [coe_eq_castSucc, castSucc_lt_castSucc_iff]
 
 #align fin.coe_succ_eq_succ Fin.coeSucc_eq_succ
 

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -1042,7 +1042,7 @@ theorem castSucc_zero' [NeZero n] : castSucc (0 : Fin n) = 0 :=
 /-- `castSucc i` is positive when `i` is positive.
 
 The `Fin.castSucc_pos` in `Std` only applies in `Fin (n+1)`.
-This one instead uses a `NeZero n` typeclass hypothesis.-/
+This one instead uses a `NeZero n` typeclass hypothesis. -/
 theorem castSucc_pos' [NeZero n] {i : Fin n} (h : 0 < i) : 0 < castSucc i := by
   simpa [lt_iff_val_lt_val] using h
 #align fin.cast_succ_pos Fin.castSucc_pos'

Scatter the content of Data.Nat.Basic across:

• Data.Nat.Defs for the lemmas having no dependencies
• Algebra.Group.Nat for the monoid instances and the few miscellaneous lemmas needing them.
• Algebra.Ring.Nat for the semiring instance and the few miscellaneous lemmas following it.

Similarly, scatter

• Data.Int.Basic across Data.Int.Defs, Algebra.Group.Int, Algebra.Ring.Int
• Data.Nat.Order.Basic across Data.Nat.Defs, Algebra.Order.Group.Nat, Algebra.Order.Ring.Nat
• Data.Int.Order.Basic across Data.Int.Defs, Algebra.Order.Group.Int, Algebra.Order.Ring.Int

Also move a few lemmas from Data.Nat.Order.Lemmas to Data.Nat.Defs.

Before

After

@@ -5,7 +5,7 @@ Authors: Robert Y. Lewis, Keeley Hoek
 -/
 import Mathlib.Algebra.NeZero
 import Mathlib.Order.RelIso.Basic
-import Mathlib.Data.Nat.Order.Basic
+import Mathlib.Algebra.Order.Ring.Nat
 import Mathlib.Order.Hom.Set
 import Std.Data.Fin.Lemmas
 

@@ -333,7 +333,7 @@ The `Fin.pos_iff_ne_zero` in `Std` only applies in `Fin (n+1)`.
 This one instead uses a `NeZero n` typeclass hypothesis.
 -/
 theorem pos_iff_ne_zero' [NeZero n] (a : Fin n) : 0 < a ↔ a ≠ 0 := by
-  rw [← val_fin_lt, val_zero', _root_.pos_iff_ne_zero, Ne.def, Ne.def, ext_iff, val_zero']
+  rw [← val_fin_lt, val_zero', _root_.pos_iff_ne_zero, Ne, Ne, ext_iff, val_zero']
 #align fin.pos_iff_ne_zero Fin.pos_iff_ne_zero'
 
 #align fin.eq_zero_or_eq_succ Fin.eq_zero_or_eq_succ

Add two simple results on graph colorings with χ(G) colors.

1. If r ≤ χ(G) and C is an r-coloring of G then C is surjective
2. If G has an α-coloring then χ(G) = |α| iff every such coloring is surjective.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -808,6 +808,11 @@ theorem le_zero_iff' {n : ℕ} [NeZero n] {k : Fin n} : k ≤ 0 ↔ k = 0 :=
 theorem strictMono_castLE (h : n ≤ m) : StrictMono (castLE h : Fin n → Fin m) :=
   fun _ _ h => h
 
+lemma castLE_injective (hmn : m ≤ n) : Injective (castLE hmn) := (strictMono_castLE _).injective
+
+@[simp] lemma castLE_inj {hmn : m ≤ n} {a b : Fin m} : castLE hmn a = castLE hmn b ↔ a = b :=
+  (castLE_injective _).eq_iff
+
 /-- `Fin.castLE` as an `OrderEmbedding`, `castLEEmb h i` embeds `i` into a larger `Fin` type.  -/
 @[simps! apply toEmbedding]
 def castLEEmb (h : n ≤ m) : Fin n ↪o Fin m :=

Classifies by adding issue number #10618 to porting notes claiming "simp can prove it".

@@ -544,12 +544,12 @@ instance addCommSemigroup (n : ℕ) : AddCommSemigroup (Fin n) where
   add_comm := by simp [ext_iff, add_def, add_comm]
 #align fin.add_comm_semigroup Fin.addCommSemigroup
 
--- Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
+-- Porting note (#10618): removing `simp`, `simp` can prove it with AddCommMonoid instance
 protected theorem add_zero [NeZero n] (k : Fin n) : k + 0 = k := by
   simp only [add_def, val_zero', add_zero, mod_eq_of_lt (is_lt k)]
 #align fin.add_zero Fin.add_zero
 
--- Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
+-- Porting note (#10618): removing `simp`, `simp` can prove it with AddCommMonoid instance
 protected theorem zero_add [NeZero n] (k : Fin n) : 0 + k = k := by
   simp [ext_iff, add_def, mod_eq_of_lt (is_lt k)]
 #align fin.zero_add Fin.zero_add

From sphere-eversion; I adapted the proof to mathlib's definition and golfed it a bit. This adds a new import; as this file is not imported anywhere, this seems fine.

@@ -1082,6 +1082,9 @@ theorem coe_eq_castSucc {a : Fin n} : (a : Fin (n + 1)) = castSucc a := by
   exact val_cast_of_lt (Nat.lt.step a.is_lt)
 #align fin.coe_eq_cast_succ Fin.coe_eq_castSucc
 
+theorem coe_succ_lt_iff_lt {n : ℕ} {j k : Fin n} : (j : Fin <| n + 1) < k ↔ j < k := by
+  simp only [coe_eq_castSucc]; rfl
+
 #align fin.coe_succ_eq_succ Fin.coeSucc_eq_succ
 
 #align fin.lt_succ Fin.lt_succ

Also add two missing simp attributes

@@ -673,9 +673,9 @@ theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : (a : Fin n).
   Nat.mod_eq_of_lt h
 #align fin.coe_val_of_lt Fin.val_cast_of_lt
 
-/-- Converting the value of a `Fin (n + 1)` to `Fin (n + 1)` results
+/-- If `n` is non-zero, converting the value of a `Fin n` to `Fin n` results
 in the same value.  -/
-theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a :=
+@[simp] theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a :=
   ext <| val_cast_of_lt a.isLt
 #align fin.coe_val_eq_self Fin.cast_val_eq_self
 

This PR removes the default values for nsmul and zsmul, forcing the user to populate them manually. The previous behavior can be obtained by writing nsmul := nsmulRec and zsmul := zsmulRec, which is now in the docstring for these fields.

The motivation here is to make it more obvious when module diamonds are being introduced, or at least where they might be hiding; you can now simply search for nsmulRec in the source code.

Arguably we should do the same thing for intCast, natCast, pow, and zpow too, but diamonds are less common in those fields, so I'll leave them to a subsequent PR.

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -583,6 +583,7 @@ instance (n) : AddCommSemigroup (Fin n) where
 instance addCommMonoid (n : ℕ) [NeZero n] : AddCommMonoid (Fin n) where
   zero_add := Fin.zero_add
   add_zero := Fin.add_zero
+  nsmul := nsmulRec
   __ := Fin.addCommSemigroup n
 #align fin.add_comm_monoid Fin.addCommMonoid
 
@@ -1515,7 +1516,8 @@ instance addCommGroup (n : ℕ) [NeZero n] : AddCommGroup (Fin n) :=
         exact le_of_lt ha
     sub_eq_add_neg := fun ⟨a, ha⟩ ⟨b, hb⟩ =>
       Fin.ext <| show (a + (n - b)) % n = (a + (n - b) % n) % n by simp
-    sub := Fin.sub }
+    sub := Fin.sub
+    zsmul := zsmulRec }
 
 /-- Note this is more general than `Fin.addCommGroup` as it applies (vacuously) to `Fin 0` too. -/
 instance instInvolutiveNeg (n : ℕ) : InvolutiveNeg (Fin n) where

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -7,7 +7,7 @@ import Mathlib.Algebra.NeZero
 import Mathlib.Order.RelIso.Basic
 import Mathlib.Data.Nat.Order.Basic
 import Mathlib.Order.Hom.Set
-import Std.Data.Fin.Basic
+import Std.Data.Fin.Lemmas
 
 #align_import data.fin.basic from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -151,7 +151,7 @@ theorem ne_iff_vne (a b : Fin n) : a ≠ b ↔ a.1 ≠ b.1 :=
   ext_iff.not
 #align fin.ne_iff_vne Fin.ne_iff_vne
 
--- porting note: I'm not sure if this comment still applies.
+-- Porting note: I'm not sure if this comment still applies.
 -- built-in reduction doesn't always work
 @[simp, nolint simpNF]
 theorem mk_eq_mk {a h a' h'} : @mk n a h = @mk n a' h' ↔ a = a' :=
@@ -297,7 +297,7 @@ instance {n : ℕ} : WellFoundedRelation (Fin n) :=
 def ofNat'' [NeZero n] (i : ℕ) : Fin n :=
   ⟨i % n, mod_lt _ <| NeZero.pos n⟩
 #align fin.of_nat' Fin.ofNat''ₓ
--- porting note: `Fin.ofNat'` conflicts with something in core (there the hypothesis is `n > 0`),
+-- Porting note: `Fin.ofNat'` conflicts with something in core (there the hypothesis is `n > 0`),
 -- so for now we make this double-prime `''`. This is also the reason for the dubious translation.
 
 instance {n : ℕ} [NeZero n] : Zero (Fin n) := ⟨ofNat'' 0⟩
@@ -421,7 +421,7 @@ theorem le_rev_iff {i j : Fin n} : i ≤ rev j ↔ j ≤ rev i := by
 #align fin.last Fin.last
 #align fin.coe_last Fin.val_last
 
--- porting note: this is now syntactically equal to `val_last`
+-- Porting note: this is now syntactically equal to `val_last`
 #align fin.last_val Fin.val_last
 #align fin.le_last Fin.le_last
 
@@ -465,7 +465,7 @@ theorem coe_orderIso_apply (e : Fin n ≃o Fin m) (i : Fin n) : (e i : ℕ) = i
   refine' le_antisymm (forall_lt_iff_le.1 fun j hj => _) (forall_lt_iff_le.1 fun j hj => _)
   · have := e.symm.lt_iff_lt.2 (mk_lt_of_lt_val hj)
     rw [e.symm_apply_apply] at this
-    -- porting note: convert was abusing definitional equality
+    -- Porting note: convert was abusing definitional equality
     have : _ < i := this
     convert this
     simpa using h _ this (e.symm _).is_lt
@@ -518,7 +518,7 @@ theorem val_one' (n : ℕ) [NeZero n] : ((1 : Fin n) : ℕ) = 1 % n :=
   rfl
 #align fin.coe_one' Fin.val_one'
 
---Porting note: Delete this lemma after porting
+-- Porting note: Delete this lemma after porting
 theorem val_one'' {n : ℕ} : ((1 : Fin (n + 1)) : ℕ) = 1 % (n + 1) :=
   rfl
 #align fin.one_val Fin.val_one''
@@ -531,7 +531,7 @@ instance nontrivial {n : ℕ} : Nontrivial (Fin (n + 2)) where
 theorem nontrivial_iff_two_le : Nontrivial (Fin n) ↔ 2 ≤ n := by
   rcases n with (_ | _ | n) <;>
   simp [← Nat.one_eq_succ_zero, Fin.nontrivial, not_nontrivial, Nat.succ_le_iff]
--- porting note: here and in the next lemma, had to use `← Nat.one_eq_succ_zero`.
+-- Porting note: here and in the next lemma, had to use `← Nat.one_eq_succ_zero`.
 #align fin.nontrivial_iff_two_le Fin.nontrivial_iff_two_le
 
 #align fin.subsingleton_iff_le_one Fin.subsingleton_iff_le_one
@@ -544,12 +544,12 @@ instance addCommSemigroup (n : ℕ) : AddCommSemigroup (Fin n) where
   add_comm := by simp [ext_iff, add_def, add_comm]
 #align fin.add_comm_semigroup Fin.addCommSemigroup
 
---Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
+-- Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
 protected theorem add_zero [NeZero n] (k : Fin n) : k + 0 = k := by
   simp only [add_def, val_zero', add_zero, mod_eq_of_lt (is_lt k)]
 #align fin.add_zero Fin.add_zero
 
---Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
+-- Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
 protected theorem zero_add [NeZero n] (k : Fin n) : 0 + k = k := by
   simp [ext_iff, add_def, mod_eq_of_lt (is_lt k)]
 #align fin.zero_add Fin.zero_add
@@ -653,7 +653,7 @@ end Bit
 
 #align fin.val_two Fin.val_two
 
---- porting note: syntactically the same as the above
+--- Porting note: syntactically the same as the above
 #align fin.coe_two Fin.val_two
 
 section OfNatCoe
@@ -665,7 +665,7 @@ theorem ofNat''_eq_cast (n : ℕ) [NeZero n] (a : ℕ) : (Fin.ofNat'' a : Fin n)
 
 @[simp] lemma val_nat_cast (a n : ℕ) [NeZero n] : (a : Fin n).val = a % n := rfl
 
--- porting note: is this the right name for things involving `Nat.cast`?
+-- Porting note: is this the right name for things involving `Nat.cast`?
 /-- Converting an in-range number to `Fin (n + 1)` produces a result
 whose value is the original number.  -/
 theorem val_cast_of_lt {n : ℕ} [NeZero n] {a : ℕ} (h : a < n) : (a : Fin n).val = a :=
@@ -678,10 +678,10 @@ theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a
   ext <| val_cast_of_lt a.isLt
 #align fin.coe_val_eq_self Fin.cast_val_eq_self
 
--- porting note: this is syntactically the same as `val_cast_of_lt`
+-- Porting note: this is syntactically the same as `val_cast_of_lt`
 #align fin.coe_coe_of_lt Fin.val_cast_of_lt
 
--- porting note: this is syntactically the same as `cast_val_of_lt`
+-- Porting note: this is syntactically the same as `cast_val_of_lt`
 #align fin.coe_coe_eq_self Fin.cast_val_eq_self
 
 @[simp] lemma nat_cast_self (n : ℕ) [NeZero n] : (n : Fin n) = 0 := by ext; simp

We have Fin.eq_of_val_eq and Fin.val_eq_of_eq in Lean core now. Also slightly shake the tree.

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Keeley Hoek
 -/
 import Mathlib.Algebra.NeZero
-import Mathlib.Init.Data.Fin.Basic
 import Mathlib.Order.RelIso.Basic
 import Mathlib.Data.Nat.Order.Basic
 import Mathlib.Order.Hom.Set
@@ -100,7 +99,7 @@ variable {n m : ℕ}
 #align fin.fin_to_nat Fin.coeToNat
 
 theorem val_injective : Function.Injective (@Fin.val n) :=
-  @Fin.eq_of_veq n
+  @Fin.eq_of_val_eq n
 #align fin.val_injective Fin.val_injective
 
 /-- If you actually have an element of `Fin n`, then the `n` is always positive -/
@@ -143,12 +142,13 @@ theorem val_eq_val (a b : Fin n) : (a : ℕ) = b ↔ a = b :=
   ext_iff.symm
 #align fin.coe_eq_coe Fin.val_eq_val
 
+@[deprecated ext_iff] -- 2024-02-20
 theorem eq_iff_veq (a b : Fin n) : a = b ↔ a.1 = b.1 :=
-  ⟨veq_of_eq, eq_of_veq⟩
+  ext_iff
 #align fin.eq_iff_veq Fin.eq_iff_veq
 
 theorem ne_iff_vne (a b : Fin n) : a ≠ b ↔ a.1 ≠ b.1 :=
-  ⟨vne_of_ne, ne_of_vne⟩
+  ext_iff.not
 #align fin.ne_iff_vne Fin.ne_iff_vne
 
 -- porting note: I'm not sure if this comment still applies.
@@ -540,8 +540,8 @@ section Monoid
 
 instance addCommSemigroup (n : ℕ) : AddCommSemigroup (Fin n) where
   add := (· + ·)
-  add_assoc := by simp [eq_iff_veq, add_def, add_assoc]
-  add_comm := by simp [eq_iff_veq, add_def, add_comm]
+  add_assoc := by simp [ext_iff, add_def, add_assoc]
+  add_comm := by simp [ext_iff, add_def, add_comm]
 #align fin.add_comm_semigroup Fin.addCommSemigroup
 
 --Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
@@ -551,7 +551,7 @@ protected theorem add_zero [NeZero n] (k : Fin n) : k + 0 = k := by
 
 --Porting note: removing `simp`, `simp` can prove it with AddCommMonoid instance
 protected theorem zero_add [NeZero n] (k : Fin n) : 0 + k = k := by
-  simp [eq_iff_veq, add_def, mod_eq_of_lt (is_lt k)]
+  simp [ext_iff, add_def, mod_eq_of_lt (is_lt k)]
 #align fin.zero_add Fin.zero_add
 
 instance [NeZero n] : OfNat (Fin n) a where
@@ -577,8 +577,8 @@ section from_ad_hoc
 end from_ad_hoc
 
 instance (n) : AddCommSemigroup (Fin n) where
-  add_assoc := by simp [eq_iff_veq, add_def, add_assoc]
-  add_comm := by simp [eq_iff_veq, add_def, add_comm]
+  add_assoc := by simp [ext_iff, add_def, add_assoc]
+  add_comm := by simp [ext_iff, add_def, add_comm]
 
 instance addCommMonoid (n : ℕ) [NeZero n] : AddCommMonoid (Fin n) where
   zero_add := Fin.zero_add
@@ -590,7 +590,7 @@ instance instAddMonoidWithOne (n) [NeZero n] : AddMonoidWithOne (Fin n) where
   __ := inferInstanceAs (AddCommMonoid (Fin n))
   natCast n := Fin.ofNat'' n
   natCast_zero := rfl
-  natCast_succ _ := eq_of_veq (add_mod _ _ _)
+  natCast_succ _ := ext (add_mod _ _ _)
 #align fin.add_monoid_with_one Fin.instAddMonoidWithOne
 
 end Monoid
@@ -637,7 +637,7 @@ set_option linter.deprecated false
 @[simp, deprecated]
 theorem mk_bit0 {m n : ℕ} (h : bit0 m < n) :
     (⟨bit0 m, h⟩ : Fin n) = (bit0 ⟨m, (Nat.le_add_right m m).trans_lt h⟩ : Fin _) :=
-  eq_of_veq (Nat.mod_eq_of_lt h).symm
+  eq_of_val_eq (Nat.mod_eq_of_lt h).symm
 #align fin.mk_bit0 Fin.mk_bit0
 
 @[simp, deprecated]
@@ -687,7 +687,7 @@ theorem cast_val_eq_self {n : ℕ} [NeZero n] (a : Fin n) : (a.val : Fin n) = a
 @[simp] lemma nat_cast_self (n : ℕ) [NeZero n] : (n : Fin n) = 0 := by ext; simp
 
 @[simp] lemma nat_cast_eq_zero {a n : ℕ} [NeZero n] : (a : Fin n) = 0 ↔ n ∣ a := by
-  simp [eq_iff_veq, Nat.dvd_iff_mod_eq_zero]
+  simp [ext_iff, Nat.dvd_iff_mod_eq_zero]
 
 @[simp]
 theorem cast_nat_eq_last (n) : (n : Fin (n + 1)) = Fin.last n := by ext; simp
@@ -792,7 +792,7 @@ This one instead uses a `NeZero n` typeclass hypothesis.
 -/
 @[simp]
 theorem le_zero_iff' {n : ℕ} [NeZero n] {k : Fin n} : k ≤ 0 ↔ k = 0 :=
-  ⟨fun h => Fin.eq_of_veq <| by rw [Nat.eq_zero_of_le_zero h]; rfl, by rintro rfl; exact le_refl _⟩
+  ⟨fun h => Fin.ext <| by rw [Nat.eq_zero_of_le_zero h]; rfl, by rintro rfl; exact le_rfl⟩
 #align fin.le_zero_iff Fin.le_zero_iff'
 
 #align fin.succ_succ_ne_one Fin.succ_succ_ne_one
@@ -868,10 +868,10 @@ theorem coe_of_injective_castLEEmb_symm {n k : ℕ} (h : n ≤ k) (i : Fin k) (h
 #align fin.cast_le_comp_cast_le Fin.castLE_comp_castLE
 
 theorem leftInverse_cast (eq : n = m) : LeftInverse (cast eq.symm) (cast eq) :=
-  fun _ => eq_of_veq rfl
+  fun _ => rfl
 
 theorem rightInverse_cast (eq : n = m) : RightInverse (cast eq.symm) (cast eq) :=
-  fun _ => eq_of_veq rfl
+  fun _ => rfl
 
 theorem cast_le_cast (eq : n = m) {a b : Fin n} : cast eq a ≤ cast eq b ↔ a ≤ b :=
   Iff.rfl
@@ -1675,7 +1675,7 @@ protected theorem mul_one' [NeZero n] (k : Fin n) : k * 1 = k := by
   · simp [eq_iff_true_of_subsingleton]
   cases n
   · simp [fin_one_eq_zero]
-  simp [eq_iff_veq, mul_def, mod_eq_of_lt (is_lt k)]
+  simp [ext_iff, mul_def, mod_eq_of_lt (is_lt k)]
 #align fin.mul_one Fin.mul_one'
 
 #align fin.mul_comm Fin.mul_comm
@@ -1684,11 +1684,11 @@ protected theorem one_mul' [NeZero n] (k : Fin n) : (1 : Fin n) * k = k := by
   rw [Fin.mul_comm, Fin.mul_one']
 #align fin.one_mul Fin.one_mul'
 
-protected theorem mul_zero' [NeZero n] (k : Fin n) : k * 0 = 0 := by simp [eq_iff_veq, mul_def]
+protected theorem mul_zero' [NeZero n] (k : Fin n) : k * 0 = 0 := by simp [ext_iff, mul_def]
 #align fin.mul_zero Fin.mul_zero'
 
 protected theorem zero_mul' [NeZero n] (k : Fin n) : (0 : Fin n) * k = 0 := by
-  simp [eq_iff_veq, mul_def]
+  simp [ext_iff, mul_def]
 #align fin.zero_mul Fin.zero_mul'
 
 end Mul

Fin.elim0 and Fin.elim0' are exactly the same function (non-dependent eliminator for Fin 0) and we were missing the dependent version (I suspect that Fin.elim0 originally was dependent, and became non-dependent upon landing in Std).

From PFR

@@ -89,10 +89,10 @@ namespace Fin
 instance : CanLift ℕ (Fin n) Fin.val (· < n) where
   prf k hk := ⟨⟨k, hk⟩, rfl⟩
 
-/-- A non-dependent variant of `elim0`. -/
-def elim0' {α : Sort*} (x : Fin 0) : α :=
-  x.elim0
-#align fin.elim0' Fin.elim0'
+/-- A dependent variant of `Fin.elim0`. -/
+def rec0 {α : Fin 0 → Sort*} (i : Fin 0) : α i := absurd i.2 (Nat.not_lt_zero _)
+
+#align fin.elim0' Fin.elim0
 
 variable {n m : ℕ}
 --variable {a b : Fin n} -- this *really* breaks stuff

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -236,11 +236,11 @@ instance {n : ℕ} : LinearOrder (Fin n) :=
 #align fin.mk_le_mk Fin.mk_le_mk
 #align fin.mk_lt_mk Fin.mk_lt_mk
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem min_val {a : Fin n} : min (a : ℕ) n = a := by simp
 #align fin.min_coe Fin.min_val
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem max_val {a : Fin n} : max (a : ℕ) n = n := by simp
 #align fin.max_coe Fin.max_val
 

The new proof is longer but I need this lemma before Fintype for a future refactor, see #9794

@@ -817,6 +817,29 @@ def castLEEmb (h : n ≤ m) : Fin n ↪o Fin m :=
 #align fin.cast_le_mk Fin.castLE_mk
 #align fin.cast_le_zero Fin.castLE_zero
 
+/- The next proof can be golfed a lot using `Fintype.card`.
+It is written this way to define `ENat.card` and `Nat.card` without a `Fintype` dependency
+(not done yet). -/
+assert_not_exists Fintype
+
+lemma nonempty_embedding_iff : Nonempty (Fin n ↪ Fin m) ↔ n ≤ m := by
+  refine ⟨fun h ↦ ?_, fun h ↦ ⟨(castLEEmb h).toEmbedding⟩⟩
+  induction n generalizing m with
+  | zero => exact m.zero_le
+  | succ n ihn =>
+    cases' h with e
+    rcases exists_eq_succ_of_ne_zero (pos_iff_nonempty.2 (Nonempty.map e inferInstance)).ne'
+      with ⟨m, rfl⟩
+    refine Nat.succ_le_succ <| ihn ⟨?_⟩
+    refine ⟨fun i ↦ (e.setValue 0 0 i.succ).pred (mt e.setValue_eq_iff.1 i.succ_ne_zero),
+      fun i j h ↦ ?_⟩
+    simpa only [pred_inj, EmbeddingLike.apply_eq_iff_eq, succ_inj] using h
+
+lemma equiv_iff_eq : Nonempty (Fin m ≃ Fin n) ↔ m = n :=
+  ⟨fun ⟨e⟩ ↦ le_antisymm (nonempty_embedding_iff.1 ⟨e⟩) (nonempty_embedding_iff.1 ⟨e.symm⟩),
+    fun h ↦ h ▸ ⟨.refl _⟩⟩
+#align fin.equiv_iff_eq Fin.equiv_iff_eq
+
 @[simp] lemma castLE_castSucc {n m} (i : Fin n) (h : n + 1 ≤ m) :
     i.castSucc.castLE h = i.castLE (Nat.le_of_succ_le h) :=
   rfl

This removes the following files from the import closure of Data.Fin.Basic:

Mathlib.Algebra.Group.Equiv.Basic
Mathlib.Algebra.Group.Hom.Basic
Mathlib.Algebra.Group.InjSurj
Mathlib.Algebra.Group.OrderSynonym
Mathlib.Algebra.Group.Units.Equiv
Mathlib.Algebra.Group.Units.Hom
Mathlib.Algebra.GroupWithZero.Basic
Mathlib.Algebra.GroupWithZero.InjSurj
Mathlib.Algebra.GroupWithZero.Units.Basic
Mathlib.Algebra.GroupWithZero.Units.Equiv
Mathlib.Algebra.Order.Group.Units
Mathlib.Algebra.Order.Monoid.Basic
Mathlib.Algebra.Order.Monoid.OrderDual
Mathlib.Algebra.Order.Monoid.TypeTags
Mathlib.Algebra.Order.Monoid.Units
Mathlib.Algebra.Order.WithZero
Mathlib.Data.Int.Cast.Basic

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Keeley Hoek
 -/
 import Mathlib.Algebra.NeZero
-import Mathlib.Algebra.Order.WithZero
 import Mathlib.Init.Data.Fin.Basic
 import Mathlib.Order.RelIso.Basic
 import Mathlib.Data.Nat.Order.Basic
@@ -1488,10 +1487,9 @@ instance neg (n : ℕ) : Neg (Fin n) :=
 instance addCommGroup (n : ℕ) [NeZero n] : AddCommGroup (Fin n) :=
   { Fin.addCommMonoid n, Fin.neg n with
     add_left_neg := fun ⟨a, ha⟩ =>
-      Fin.ext <|
-        _root_.trans (Nat.mod_add_mod _ _ _) <| by
-          rw [Fin.val_zero', tsub_add_cancel_of_le, Nat.mod_self]
-          exact le_of_lt ha
+      Fin.ext <| (Nat.mod_add_mod _ _ _).trans <| by
+        rw [Fin.val_zero', Nat.sub_add_cancel, Nat.mod_self]
+        exact le_of_lt ha
     sub_eq_add_neg := fun ⟨a, ha⟩ ⟨b, hb⟩ =>
       Fin.ext <| show (a + (n - b)) % n = (a + (n - b) % n) % n by simp
     sub := Fin.sub }
@@ -1550,7 +1548,7 @@ theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a
   · simp
   split_ifs with h
   · simp [h]
-  rw [sub_eq_add_neg, val_add_eq_ite, coe_neg_one, if_pos, add_comm, add_tsub_add_eq_tsub_left]
+  rw [sub_eq_add_neg, val_add_eq_ite, coe_neg_one, if_pos, add_comm, Nat.add_sub_add_left]
   conv_rhs => rw [add_comm]
   rw [add_le_add_iff_left, Nat.one_le_iff_ne_zero]
   rwa [Fin.ext_iff] at h

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -1555,29 +1555,7 @@ theorem coe_sub_one {n} (a : Fin (n + 1)) : ↑(a - 1) = if a = 0 then n else a
   rw [add_le_add_iff_left, Nat.one_le_iff_ne_zero]
   rwa [Fin.ext_iff] at h
 #align fin.coe_sub_one Fin.coe_sub_one
-
-theorem coe_sub_iff_le {n : ℕ} {a b : Fin n} : (↑(a - b) : ℕ) = a - b ↔ b ≤ a := by
-  cases n; · exact @finZeroElim (fun _ => _) a
-  rw [le_iff_val_le_val, Fin.coe_sub, ← add_tsub_assoc_of_le b.is_lt.le a]
-  rcases le_or_lt (b : ℕ) a with h | h
-  · simp [← tsub_add_eq_add_tsub h, val_fin_le.mp h,
-      Nat.mod_eq_of_lt ((Nat.sub_le _ _).trans_lt a.is_lt)]
-  · rw [Nat.mod_eq_of_lt, tsub_eq_zero_of_le h.le, tsub_eq_zero_iff_le, ← not_iff_not]
-    · simpa [b.is_lt.trans_le le_add_self] using h
-    · rwa [tsub_lt_iff_left (b.is_lt.le.trans le_add_self), add_lt_add_iff_right]
 #align fin.coe_sub_iff_le Fin.coe_sub_iff_le
-
-theorem coe_sub_iff_lt {n : ℕ} {a b : Fin n} : (↑(a - b) : ℕ) = n + a - b ↔ a < b := by
-  cases' n with n
-  · exact @finZeroElim (fun _ => _) a
-  rw [lt_iff_val_lt_val, Fin.coe_sub, add_comm]
-  rcases le_or_lt (b : ℕ) a with h | h
-  · refine iff_of_false ?_ (not_lt_of_le h)
-    simpa [add_tsub_assoc_of_le h] using
-      ((Nat.mod_lt _ (Nat.succ_pos _)).trans_le le_self_add).ne
-  · simp [← tsub_tsub_assoc b.is_lt.le h.le, ← tsub_add_eq_add_tsub b.is_lt.le,
-      Nat.mod_eq_of_lt (tsub_lt_self (Nat.succ_pos _) (tsub_pos_of_lt h)), val_fin_le.mp _]
-    exact h
 #align fin.coe_sub_iff_lt Fin.coe_sub_iff_lt
 
 @[simp]

Adds Fin.exists_fin_succ', which is analogous to Fin.forall_fin_succ'.

@@ -996,6 +996,11 @@ theorem forall_fin_succ' {P : Fin (n + 1) → Prop} :
 theorem eq_castSucc_or_eq_last {n : Nat} (i : Fin (n + 1)) :
     (∃ j : Fin n, i = j.castSucc) ∨ i = last n := i.lastCases (Or.inr rfl) (Or.inl ⟨·, rfl⟩)
 
+theorem exists_fin_succ' {P : Fin (n + 1) → Prop} :
+    (∃ i, P i) ↔ (∃ i : Fin n, P i.castSucc) ∨ P (.last _) :=
+  ⟨fun ⟨i, h⟩ => Fin.lastCases Or.inr (fun i hi => Or.inl ⟨i, hi⟩) i h,
+   fun h => h.elim (fun ⟨i, hi⟩ => ⟨i.castSucc, hi⟩) (fun h => ⟨.last _, h⟩)⟩
+
 /--
 The `Fin.castSucc_zero` in `Std` only applies in `Fin (n+1)`.
 This one instead uses a `NeZero n` typeclass hypothesis.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Alex Keizer <alex@keizer.dev> Co-authored-by: Tobias Grosser <tobias@grosser.es>

@@ -1517,8 +1517,6 @@ protected theorem coe_neg (a : Fin n) : ((-a : Fin n) : ℕ) = (n - a) % n :=
   rfl
 #align fin.coe_neg Fin.coe_neg
 
-protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : ℕ) = (a + (n - b)) % n := by
-  cases a; cases b; rfl
 #align fin.coe_sub Fin.coe_sub
 
 theorem eq_zero (n : Fin 1) : n = 0 := Subsingleton.elim _ _

@@ -961,11 +961,11 @@ def castSuccEmb : Fin n ↪o Fin (n + 1) :=
 @[simp]
 theorem castSucc_le_castSucc_iff : castSucc a ≤ castSucc b ↔ a ≤ b := Iff.rfl
 @[simp]
-theorem succ_le_castSucc_iff : succ a ≤ castSucc b ↔ a < b :=
-  by rw [le_castSucc_iff, succ_lt_succ_iff]
+theorem succ_le_castSucc_iff : succ a ≤ castSucc b ↔ a < b := by
+  rw [le_castSucc_iff, succ_lt_succ_iff]
 @[simp]
-theorem castSucc_lt_succ_iff : castSucc a < succ b ↔ a ≤ b :=
-  by rw [castSucc_lt_iff_succ_le, succ_le_succ_iff]
+theorem castSucc_lt_succ_iff : castSucc a < succ b ↔ a ≤ b := by
+  rw [castSucc_lt_iff_succ_le, succ_le_succ_iff]
 
 theorem le_of_castSucc_lt_of_succ_lt {a b : Fin (n + 1)} {i : Fin n}
     (hl : castSucc i < a) (hu : b < succ i) : b < a := (castSucc_lt_iff_succ_le.mp hl).trans_lt' hu
@@ -1168,10 +1168,9 @@ theorem monotone_pred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f
 
 #align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castₓ
 
-theorem pred_one' [NeZero n] (h := (zero_ne_one' (n := n)).symm):
-    Fin.pred (1 : Fin (n + 1)) h = 0 :=
-    by simp_rw [Fin.ext_iff, coe_pred, val_one', val_zero',
-      tsub_eq_zero_iff_le, Nat.mod_le]
+theorem pred_one' [NeZero n] (h := (zero_ne_one' (n := n)).symm) :
+    Fin.pred (1 : Fin (n + 1)) h = 0 := by
+  simp_rw [Fin.ext_iff, coe_pred, val_one', val_zero', tsub_eq_zero_iff_le, Nat.mod_le]
 
 theorem pred_last (h := last_pos'.ne') :
     pred (last (n + 1)) h = last n := by simp_rw [← succ_last, pred_succ]

Move succAbove and predAbove to their own file, updating their documentation and adding an OrderHom instance for predAbove, predAboveOrderHom.

@@ -55,8 +55,7 @@ This file expands on the development in the core library.
   provided that `n = m`, see also `Equiv.finCongr`;
 * `Fin.castAddEmb m` : `Fin.castAdd` as an `OrderEmbedding`, embed `Fin n` into `Fin (n+m)`;
 * `Fin.castSuccEmb` : `Fin.castSucc` as an `OrderEmbedding`, embed `Fin n` into `Fin (n+1)`;
-* `Fin.succAboveEmb p` : `Fin.succAbove` as an `OrderEmbedding`, embed `Fin n` into `Fin (n + 1)`
-  with a hole around `p`;
+
 * `Fin.addNatEmb m i` : `Fin.addNat` as an `OrderEmbedding`, add `m` on `i` on the right,
   generalizes `Fin.succ`;
 * `Fin.natAddEmb n i` : `Fin.natAdd` as an `OrderEmbedding`, adds `n` on `i` on the left;
@@ -989,6 +988,14 @@ theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
 #align fin.cast_succ_inj Fin.castSucc_inj
 #align fin.cast_succ_lt_last Fin.castSucc_lt_last
 
+theorem forall_fin_succ' {P : Fin (n + 1) → Prop} :
+    (∀ i, P i) ↔ (∀ i : Fin n, P i.castSucc) ∧ P (.last _) :=
+  ⟨fun H => ⟨fun _ => H _, H _⟩, fun ⟨H0, H1⟩ i => Fin.lastCases H1 H0 i⟩
+
+-- to match `Fin.eq_zero_or_eq_succ`
+theorem eq_castSucc_or_eq_last {n : Nat} (i : Fin (n + 1)) :
+    (∃ j : Fin n, i = j.castSucc) ∨ i = last n := i.lastCases (Or.inr rfl) (Or.inl ⟨·, rfl⟩)
+
 /--
 The `Fin.castSucc_zero` in `Std` only applies in `Fin (n+1)`.
 This one instead uses a `NeZero n` typeclass hypothesis.
@@ -1645,522 +1652,6 @@ lemma pos_of_ne_zero {n : ℕ} {a : Fin (n + 1)} (h : a ≠ 0) :
 
 end AddGroup
 
-section SuccAbove
-
-/-- `succAbove p i` embeds `Fin n` into `Fin (n + 1)` with a hole around `p`. -/
-def succAbove (p : Fin (n + 1)) (i : Fin n) : Fin (n + 1) :=
-  if castSucc i < p then i.castSucc else i.succ
-
-/-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
-embeds `i` by `castSucc` when the resulting `i.castSucc < p`. -/
-theorem succAbove_of_castSucc_lt (p : Fin (n + 1)) (i : Fin n) (h : castSucc i < p) :
-    p.succAbove i = castSucc i := if_pos h
-#align fin.succ_above_below Fin.succAbove_of_castSucc_lt
-
-theorem succAbove_of_succ_le (p : Fin (n + 1)) (i : Fin n) (h : succ i ≤ p) :
-    p.succAbove i = castSucc i :=
-  succAbove_of_castSucc_lt _ _ (castSucc_lt_iff_succ_le.mpr h)
-
-/-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
-embeds `i` by `succ` when the resulting `p < i.succ`. -/
-theorem succAbove_of_le_castSucc (p : Fin (n + 1)) (i : Fin n) (h : p ≤ castSucc i) :
-    p.succAbove i = i.succ := if_neg h.not_lt
-#align fin.succ_above_above Fin.succAbove_of_le_castSucc
-
-theorem succAbove_of_lt_succ (p : Fin (n + 1)) (i : Fin n) (h : p < succ i) :
-    p.succAbove i = succ i := succAbove_of_le_castSucc _ _ (le_castSucc_iff.mpr h)
-
-theorem succAbove_succ_of_lt (p i : Fin n) (h : p < i) :
-    succAbove p.succ i = i.succ := succAbove_of_lt_succ _ _ (succ_lt_succ_iff.mpr h)
-theorem succAbove_succ_of_le (p i : Fin n) (h : i ≤ p) :
-    succAbove p.succ i = i.castSucc := succAbove_of_succ_le _ _ (succ_le_succ_iff.mpr h)
-@[simp]
-theorem succAbove_succ_self (j : Fin n) : j.succ.succAbove j = j.castSucc :=
-  succAbove_succ_of_le _ _ le_rfl
-
-theorem succAbove_castSucc_of_lt (p i : Fin n) (h : i < p) :
-    succAbove p.castSucc i = i.castSucc :=
-  succAbove_of_castSucc_lt _ _ (castSucc_lt_castSucc_iff.mpr h)
-theorem succAbove_castSucc_of_le (p i : Fin n) (h : p ≤ i) :
-    succAbove p.castSucc i = i.succ :=
-  succAbove_of_le_castSucc _ _ (castSucc_le_castSucc_iff.mpr h)
-@[simp]
-theorem succAbove_castSucc_self (j : Fin n) : succAbove j.castSucc j = j.succ :=
-  succAbove_castSucc_of_le _ _ le_rfl
-
-theorem succAbove_pred_of_lt (p i : Fin (n + 1)) (h : p < i) (hi := ((zero_le p).trans_lt h).ne') :
-    succAbove p (i.pred hi) = i := by
-  rw [succAbove_of_lt_succ _ _ (succ_pred _ _ ▸ h), succ_pred]
-theorem succAbove_pred_of_le (p i : Fin (n + 1)) (h : i ≤ p) (hi : i ≠ 0):
-    succAbove p (i.pred hi) = (i.pred hi).castSucc := succAbove_of_succ_le _ _ (succ_pred _ _ ▸ h)
-@[simp]
-theorem succAbove_pred_self (p : Fin (n + 1)) (h : p ≠ 0) :
-    succAbove p (p.pred h) = (p.pred h).castSucc := succAbove_pred_of_le _ _ le_rfl h
-
-theorem succAbove_castPred_of_lt (p i : Fin (n + 1)) (h : i < p)
-    (hi := ((le_last p).trans_lt' h).ne) : succAbove p (i.castPred hi) = i := by
-  rw [succAbove_of_castSucc_lt _ _ (castSucc_castPred _ _ ▸ h), castSucc_castPred]
-theorem succAbove_castPred_of_le (p i : Fin (n + 1)) (h : p ≤ i) (hi : i ≠ last n):
-    succAbove p (i.castPred hi) = (i.castPred hi).succ :=
-  succAbove_of_le_castSucc _ _ (castSucc_castPred _ _ ▸ h)
-theorem succAbove_castPred_self (p : Fin (n + 1)) (h: p ≠ last n):
-    succAbove p (p.castPred h) = (p.castPred h).succ :=
-  succAbove_castPred_of_le _ _ le_rfl h
-
-theorem succAbove_rev_left (p : Fin (n + 1)) (i : Fin n) :
-    p.rev.succAbove i = (p.succAbove i.rev).rev := by
-  obtain h | h := (rev p).succ_le_or_le_castSucc i
-  · rw [succAbove_of_succ_le _ _ h,
-      succAbove_of_le_castSucc _ _ (rev_succ _ ▸ (le_rev_iff.mpr h)), rev_succ, rev_rev]
-  · rw [succAbove_of_le_castSucc _ _ h,
-      succAbove_of_succ_le _ _ (rev_castSucc _ ▸ (rev_le_iff.mpr h)), rev_castSucc, rev_rev]
-theorem succAbove_rev_right (p : Fin (n + 1)) (i : Fin n) :
-    p.succAbove i.rev = (p.rev.succAbove i).rev := by
-  rw [succAbove_rev_left, rev_rev]
-
-/-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
-never results in `p` itself -/
-theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p := by
-  rcases p.castSucc_lt_or_lt_succ i with (h | h)
-  · rw [succAbove_of_castSucc_lt _ _ h]
-    exact h.ne
-  · rw [succAbove_of_lt_succ _ _ h]
-    exact h.ne'
-#align fin.succ_above_ne Fin.succAbove_ne
-theorem ne_succAbove (p : Fin (n + 1)) (i : Fin n) : p ≠ p.succAbove i :=
-(succAbove_ne _ _).symm
-
-theorem strictMono_succAbove (p : Fin (n + 1)) : StrictMono (succAbove p) :=
-  strictMono_castSucc.ite strictMono_succ
-    (fun _ _ hij hj => (castSucc_lt_castSucc_iff.mpr hij).trans hj) fun i =>
-    (castSucc_lt_succ i).le
-#align fin.succ_above_aux Fin.strictMono_succAbove
-
-/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
-theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
-  (strictMono_succAbove x).injective
-#align fin.succ_above_right_injective Fin.succAbove_right_injective
-
-/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
-theorem succAbove_right_inj (x : Fin (n + 1)) : x.succAbove a = x.succAbove b ↔ a = b :=
-  succAbove_right_injective.eq_iff
-#align fin.succ_above_right_inj Fin.succAbove_right_inj
-
-theorem succAbove_lt_succAbove_iff (p : Fin (n + 1)) :
-    succAbove p i < succAbove p j ↔ i < j := (strictMono_succAbove p).lt_iff_lt
-theorem succAbove_le_succAbove_iff (p : Fin (n + 1)) :
-    succAbove p i ≤ succAbove p j ↔ i ≤ j := (strictMono_succAbove p).le_iff_le
-
-/--  `Fin.succAbove` as an `OrderEmbedding`, `succAboveEmb p i` embeds `Fin n` into `Fin (n + 1)`
-with a hole around `p`. -/
-@[simps! apply toEmbedding]
-def succAboveEmb (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
-  OrderEmbedding.ofStrictMono (succAbove p) (strictMono_succAbove p)
-#align fin.succ_above Fin.succAboveEmb
-
-@[simp]
-theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 := by
-  rw [Fin.succAbove_of_castSucc_lt]
-  · exact castSucc_zero'
-  · exact bot_lt_iff_ne_bot.mpr ha
-#align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zero
-
-theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) :
-    a.succAbove b = 0 ↔ b = 0 := by
-  rw [← succAbove_ne_zero_zero ha, succAbove_right_inj]
-#align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iff
-
-theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) (hb : b ≠ 0) :
-    a.succAbove b ≠ 0 :=
-  mt (succAbove_eq_zero_iff ha).mp hb
-#align fin.succ_above_ne_zero Fin.succAbove_ne_zero
-
-/-- Embedding `Fin n` into `Fin (n + 1)` with a hole around zero embeds by `succ`. -/
-@[simp]
-theorem succAbove_zero : succAbove (0 : Fin (n + 1)) = Fin.succ :=
-  rfl
-#align fin.succ_above_zero Fin.succAbove_zero
-
-theorem succAbove_zero_apply (i : Fin n) : succAbove 0 i = succ i := by rw [succAbove_zero]
-
-@[simp]
-theorem succAbove_ne_last_last {a : Fin (n + 2)} (h : a ≠ last (n + 1)) :
-    a.succAbove (last n) = last (n + 1) := by
-  rw [succAbove_of_lt_succ _ _ (succ_last _ ▸ lt_top_iff_ne_top.mpr h), succ_last]
-
-theorem succAbove_eq_last_iff {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ last _) :
-    a.succAbove b = last _ ↔ b = last _ := by
-  simp [← succAbove_ne_last_last ha, succAbove_right_inj]
-
-theorem succAbove_ne_last {a : Fin (n + 2)} {b : Fin (n + 1)}
-    (ha : a ≠ last _) (hb : b ≠ last _) : a.succAbove b ≠ last _ :=
-  mt (succAbove_eq_last_iff ha).mp hb
-
-/-- Embedding `Fin n` into `Fin (n + 1)` with a hole around `last n` embeds by `castSucc`. -/
-@[simp]
-theorem succAbove_last : succAbove (Fin.last n) = castSucc := by
-  ext
-  simp only [succAbove_of_castSucc_lt, castSucc_lt_last]
-#align fin.succ_above_last Fin.succAbove_last
-
-theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = castSucc i := by
-  rw [succAbove_last]
-#align fin.succ_above_last_apply Fin.succAbove_last_apply
-
-@[deprecated] theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) :
-    castSucc i < p ∨ p ≤ castSucc i := lt_or_ge (castSucc i) p
-#align fin.succ_above_lt_ge Fin.succAbove_lt_ge
-
-@[deprecated castSucc_lt_or_lt_succ] alias succAbove_lt_gt := castSucc_lt_or_lt_succ
-
-/-- Embedding `i : Fin n` into `Fin (n + 1)` using a pivot `p` that is greater
-results in a value that is less than `p`. -/
-theorem succAbove_lt_iff_castSucc_lt (p : Fin (n + 1)) (i : Fin n) :
-    p.succAbove i < p ↔ castSucc i < p := by
-  cases' castSucc_lt_or_lt_succ p i with H H
-  · rwa [iff_true_right H, succAbove_of_castSucc_lt _ _ H]
-  · rw [castSucc_lt_iff_succ_le, iff_false_right H.not_le, succAbove_of_lt_succ _ _ H]
-    exact H.le.not_lt
-#align fin.succ_above_lt_iff Fin.succAbove_lt_iff_castSucc_lt
-
-theorem succAbove_lt_iff_succ_le (p : Fin (n + 1)) (i : Fin n) :
-    p.succAbove i < p ↔ succ i ≤ p := by
-  rw [succAbove_lt_iff_castSucc_lt, castSucc_lt_iff_succ_le]
-
-/-- Embedding `i : Fin n` into `Fin (n + 1)` using a pivot `p` that is lesser
-results in a value that is greater than `p`. -/
-theorem lt_succAbove_iff_le_castSucc (p : Fin (n + 1)) (i : Fin n) :
-    p < p.succAbove i ↔ p ≤ castSucc i := by
-  cases' castSucc_lt_or_lt_succ p i with H H
-  · rw [iff_false_right H.not_le, succAbove_of_castSucc_lt _ _ H]
-    exact H.le.not_lt
-  · rwa [succAbove_of_lt_succ _ _ H, iff_true_left H, le_castSucc_iff]
-#align fin.lt_succ_above_iff Fin.lt_succAbove_iff_le_castSucc
-
-theorem lt_succAbove_iff_lt_castSucc (p : Fin (n + 1)) (i : Fin n) :
-    p < p.succAbove i ↔ p < succ i := by
-  rw [lt_succAbove_iff_le_castSucc, le_castSucc_iff]
-
-/-- Embedding a positive `Fin n` results in a positive `Fin (n + 1)` -/
-theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i := by
-  by_cases H : castSucc i < p
-  · simpa [succAbove_of_castSucc_lt _ _ H] using castSucc_pos' h
-  · simp [succAbove_of_le_castSucc _ _ (le_of_not_lt H)]
-#align fin.succ_above_pos Fin.succAbove_pos
-
-theorem castPred_succAbove (x : Fin n) (y : Fin (n + 1)) (h : castSucc x < y)
-    (h' := ((le_last y).trans_lt' ((succAbove_lt_iff_castSucc_lt _ _).mpr h)).ne) :
-    (y.succAbove x).castPred h' = x := by
-  rw [castPred_eq_iff_eq_castSucc, succAbove_of_castSucc_lt _ _ h]
-#align fin.cast_lt_succ_above Fin.castPred_succAbove
-
-theorem pred_succAbove (x : Fin n) (y : Fin (n + 1)) (h : y ≤ castSucc x)
-    (h' := (y.zero_le.trans_lt <| (lt_succAbove_iff_le_castSucc _ _).2 h).ne') :
-    (y.succAbove x).pred h' = x := by simp only [succAbove_of_le_castSucc _ _ h, pred_succ]
-#align fin.pred_succ_above Fin.pred_succAbove
-
-theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x := by
-  cases' h.lt_or_lt with hlt hlt
-  exacts [⟨_, succAbove_castPred_of_lt _ _ hlt⟩, ⟨_, succAbove_pred_of_lt _ _ hlt⟩]
-#align fin.exists_succ_above_eq Fin.exists_succAbove_eq
-
-@[simp]
-theorem exists_succAbove_eq_iff {x y : Fin (n + 1)} : (∃ z, x.succAbove z = y) ↔ y ≠ x := by
-  refine' ⟨_, exists_succAbove_eq⟩
-  rintro ⟨y, rfl⟩
-  exact succAbove_ne _ _
-#align fin.exists_succ_above_eq_iff Fin.exists_succAbove_eq_iff
-
-/-- The range of `p.succAbove` is everything except `p`. -/
-@[simp]
-theorem range_succAbove (p : Fin (n + 1)) : Set.range p.succAbove = {p}ᶜ :=
-  Set.ext fun _ => exists_succAbove_eq_iff
-#align fin.range_succ_above Fin.range_succAbove
-
-@[simp]
-theorem range_succ (n : ℕ) : Set.range (Fin.succ : Fin n → Fin (n + 1)) = {0}ᶜ := by
-  rw [← succAbove_zero]
-  exact range_succAbove (0 : Fin (n + 1))
-#align fin.range_succ Fin.range_succ
-
-/-- `succAbove` is injective at the pivot -/
-theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
-  simpa [range_succAbove] using congr_arg (fun f : Fin n → Fin (n + 1) => (Set.range f)ᶜ) h
-#align fin.succ_above_left_injective Fin.succAbove_left_injective
-
-/-- `succAbove` is injective at the pivot -/
-@[simp]
-theorem succAbove_left_inj {x y : Fin (n + 1)} : x.succAbove = y.succAbove ↔ x = y :=
-  succAbove_left_injective.eq_iff
-#align fin.succ_above_left_inj Fin.succAbove_left_inj
-
-@[simp]
-theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i.succ := by
-  rfl
-#align fin.zero_succ_above Fin.zero_succAbove
-
-@[simp]
-theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : succAbove i.succ 0 = 0 :=
-  succAbove_of_castSucc_lt i.succ 0 (by simp only [castSucc_zero', succ_pos])
-#align fin.succ_succ_above_zero Fin.succ_succAbove_zero
-
-/-- `succ` commutes with `succAbove`. -/
-@[simp]
-theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
-    i.succ.succAbove j.succ = (i.succAbove j).succ := by
-  rcases lt_or_le i (succ j) with (h | h)
-  · rw [succAbove_of_lt_succ _ _ h, succAbove_succ_of_lt _ _ h]
-  · rwa [succAbove_of_castSucc_lt _ _ h, succAbove_succ_of_le, succ_castSucc]
-#align fin.succ_succ_above_succ Fin.succ_succAbove_succ
-
-/-- `castSucc` commutes with `succAbove`. -/
-@[simp]
-theorem castSucc_succAbove_castSucc {n : ℕ} {i : Fin (n + 1)} {j : Fin n} :
-    i.castSucc.succAbove j.castSucc = (i.succAbove j).castSucc := by
-  rcases le_or_lt i (castSucc j) with (h | h)
-  · rw [succAbove_of_le_castSucc _ _ h, succAbove_castSucc_of_le _ _ h, succ_castSucc]
-  · rw [succAbove_of_castSucc_lt _ _ h, succAbove_castSucc_of_lt _ _ h]
-
-/-- `pred` commutes with `succAbove`. -/
-theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
-    (hk := succAbove_ne_zero ha hb) :
-    (a.pred ha).succAbove (b.pred hb) = (a.succAbove b).pred hk := by
-  simp_rw [← succ_inj (b := pred (succAbove a b) hk), ← succ_succAbove_succ, succ_pred]
-#align fin.pred_succ_above_pred Fin.pred_succAbove_pred
-
-/-- `castPred` commutes with `succAbove`. -/
-theorem castPred_succAbove_castPred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ last (n + 1))
-    (hb : b ≠ last n) (hk := succAbove_ne_last ha hb) :
-    (a.castPred ha).succAbove (b.castPred hb) = (a.succAbove b).castPred hk := by
-  simp_rw [← castSucc_inj (b := (a.succAbove b).castPred hk), ← castSucc_succAbove_castSucc,
-    castSucc_castPred]
-
-/-- `rev` commutes with `succAbove`. -/
-lemma rev_succAbove (p : Fin (n + 1)) (i : Fin n) :
-    rev (succAbove p i) = succAbove (rev p) (rev i) := by
-  rw [succAbove_rev_left, rev_rev]
-
---@[simp] -- porting note: can be proved by `simp`
-theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 := by
-  rfl
-#align fin.one_succ_above_zero Fin.one_succAbove_zero
-
-/-- By moving `succ` to the outside of this expression, we create opportunities for further
-simplification using `succAbove_zero` or `succ_succAbove_zero`. -/
-@[simp]
-theorem succ_succAbove_one {n : ℕ} [NeZero n] (i : Fin (n + 1)) :
-    i.succ.succAbove 1 = (i.succAbove 0).succ := by
-  rw [← succ_zero_eq_one']
-  convert succ_succAbove_succ i 0
-#align fin.succ_succ_above_one Fin.succ_succAbove_one
-
-@[simp]
-theorem one_succAbove_succ {n : ℕ} (j : Fin n) :
-    (1 : Fin (n + 2)).succAbove j.succ = j.succ.succ := by
-  have := succ_succAbove_succ 0 j
-  rwa [succ_zero_eq_one, zero_succAbove] at this
-#align fin.one_succ_above_succ Fin.one_succAbove_succ
-
-@[simp]
-theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 := by
-  have := succ_succAbove_succ (0 : Fin (n + 2)) (0 : Fin (n + 2))
-  simp only [succ_zero_eq_one, val_zero, Nat.cast_zero, zero_succAbove, succ_one_eq_two] at this
-  exact this
-#align fin.one_succ_above_one Fin.one_succAbove_one
-
-end SuccAbove
-
-section PredAbove
-
-/-- `predAbove p i` embeds `i : Fin (n+1)` into `Fin n` by subtracting one if `p < i`. -/
-def predAbove (p : Fin n) (i : Fin (n + 1)) : Fin n :=
-  if h : castSucc p < i then pred i ((zero_le _).trans_lt h).ne'
-  else castPred i ((le_of_not_lt h).trans_lt (castSucc_lt_last _)).ne
-#align fin.pred_above Fin.predAbove
-
-theorem predAbove_of_le_castSucc (p : Fin n) (i : Fin (n + 1)) (h : i ≤ castSucc p)
-    (hi := (h.trans_lt (castSucc_lt_last _)).ne) :
-    p.predAbove i = i.castPred hi := dif_neg h.not_lt
-#align fin.pred_above_below Fin.predAbove_of_le_castSucc
-theorem predAbove_of_lt_succ (p : Fin n) (i : Fin (n + 1)) (h : i < succ p)
-    (hi := ((le_last _).trans_lt' h).ne) :
-    p.predAbove i = i.castPred hi := predAbove_of_le_castSucc _ _ (le_castSucc_iff.mpr h)
-
-theorem predAbove_of_castSucc_lt (p : Fin n) (i : Fin (n + 1)) (h : castSucc p < i)
-    (hi := ((zero_le _).trans_lt h).ne') :
-    p.predAbove i = i.pred hi := dif_pos h
-#align fin.pred_above_above Fin.predAbove_of_castSucc_lt
-theorem predAbove_of_succ_le (p : Fin n) (i : Fin (n + 1)) (h : succ p ≤ i)
-    (hi := (h.trans_lt' (succ_pos _)).ne') :
-    p.predAbove i = i.pred hi := predAbove_of_castSucc_lt _ _ (castSucc_lt_iff_succ_le.mpr h)
-
-theorem predAbove_succ_of_lt (p i : Fin n) (h : i < p) (hi := succ_ne_last_of_lt h) :
-    p.predAbove (succ i) = (i.succ).castPred hi := by
-  rw [predAbove_of_lt_succ _ _ (succ_lt_succ_iff.mpr h)]
-theorem predAbove_succ_of_le (p i : Fin n) (h : p ≤ i) :
-    p.predAbove (succ i) = i := by
-  rw [predAbove_of_succ_le _ _ (succ_le_succ_iff.mpr h), pred_succ]
-@[simp]
-theorem predAbove_succ_self (p : Fin n) : p.predAbove (succ p) = p :=
-  predAbove_succ_of_le _ _ le_rfl
-
-theorem predAbove_castSucc_of_lt (p i : Fin n) (h : p < i) (hi := castSucc_ne_zero_of_lt h) :
-    p.predAbove (castSucc i) = i.castSucc.pred hi := by
-  rw [predAbove_of_castSucc_lt _ _ (castSucc_lt_castSucc_iff.mpr h)]
-theorem predAbove_castSucc_of_le (p i : Fin n) (h : i ≤ p) :
-    p.predAbove (castSucc i) = i := by
-  rw [predAbove_of_le_castSucc _ _ (castSucc_le_castSucc_iff.mpr h), castPred_castSucc]
-@[simp]
-theorem predAbove_castSucc_self (p : Fin n) : p.predAbove (castSucc p) = p :=
-  predAbove_castSucc_of_le _ _ le_rfl
-
-theorem predAbove_pred_of_lt (p i : Fin (n + 1)) (h : i < p) (hp := ((zero_le i).trans_lt h).ne')
-    (hi := ((le_last p).trans_lt' h).ne) : (pred p hp).predAbove i = castPred i hi := by
-  rw [predAbove_of_lt_succ _ _ (succ_pred _ _ ▸ h)]
-theorem predAbove_pred_of_le (p i : Fin (n + 1)) (h : p ≤ i) (hp : p ≠ 0)
-    (hi := (h.trans_lt' (pos_of_ne_zero hp)).ne') : (pred p hp).predAbove i = pred i hi := by
-  rw [predAbove_of_succ_le _ _ (succ_pred _ _ ▸ h)]
-theorem predAbove_pred_self (p : Fin (n + 1)) (hp : p ≠ 0) :
-    (pred p hp).predAbove p = pred p hp := predAbove_pred_of_le _ _ le_rfl hp
-
-theorem predAbove_castPred_of_lt (p i : Fin (n + 1)) (h : p < i)
-    (hp := ((le_last i).trans_lt' h).ne) (hi := ((zero_le p).trans_lt h).ne') :
-    (castPred p hp).predAbove i = pred i hi := by
-  rw [predAbove_of_castSucc_lt _ _ (castSucc_castPred _ _ ▸ h)]
-theorem predAbove_castPred_of_le (p i : Fin (n + 1)) (h : i ≤ p) (hp : p ≠ last n)
-    (hi := (h.trans_lt (lt_top_iff_ne_top.mpr hp)).ne) :
-    (castPred p hp).predAbove i = castPred i hi := by
-  rw [predAbove_of_le_castSucc _ _ (castSucc_castPred _ _ ▸ h)]
-theorem predAbove_castPred_self (p : Fin (n + 1)) (hp : p ≠ last n) :
-    (castPred p hp).predAbove p = castPred p hp := predAbove_castPred_of_le _ _ le_rfl hp
-
-theorem predAbove_rev_left (p : Fin n) (i : Fin (n + 1)) :
-    p.rev.predAbove i = (p.predAbove i.rev).rev := by
-  obtain h | h := (rev i).succ_le_or_le_castSucc p
-  · rw [predAbove_of_succ_le _ _ h, rev_pred,
-      predAbove_of_le_castSucc _ _ (rev_succ _ ▸ (le_rev_iff.mpr h)), castPred_inj, rev_rev]
-  · rw [predAbove_of_le_castSucc _ _ h, rev_castPred,
-      predAbove_of_succ_le _ _ (rev_castSucc _ ▸ (rev_le_iff.mpr h)), pred_inj, rev_rev]
-theorem predAbove_rev_right (p : Fin n) (i : Fin (n + 1)) :
-    p.predAbove i.rev = (p.rev.predAbove i).rev := by
-  rw [predAbove_rev_left, rev_rev]
-
-@[simp]
-theorem predAbove_right_zero [NeZero n] {i : Fin n} : predAbove (i : Fin n) 0 = 0 := by
-  cases n
-  · exact i.elim0
-  · rw [predAbove_of_le_castSucc _ _ (zero_le _), castPred_zero]
-
-@[simp]
-theorem predAbove_zero_succ [NeZero n] {i : Fin n} : predAbove 0 (i.succ) = i := by
-  rw [predAbove_succ_of_le _ _ (Fin.zero_le' _)]
-@[simp]
-theorem succ_predAbove_zero [NeZero n] {j : Fin (n + 1)} (h : j ≠ 0) :
-    succ (predAbove 0 j) = j := by
-  rcases exists_succ_eq_of_ne_zero h with ⟨k, rfl⟩
-  rw [predAbove_zero_succ]
-@[simp]
-theorem predAbove_zero_of_ne_zero [NeZero n] {i : Fin (n + 1)} (hi : i ≠ 0) :
-    predAbove 0 i = i.pred hi := by
-  rw [← exists_succ_eq] at hi
-  rcases hi with ⟨y, rfl⟩
-  exact predAbove_zero_succ
-#align fin.pred_above_zero Fin.predAbove_zero_of_ne_zero
-theorem predAbove_zero [NeZero n] :
-    predAbove (0 : Fin n) i = if hi : i = 0 then 0 else i.pred hi := by
-  split_ifs with hi
-  · rw [hi, predAbove_right_zero]
-  · rw [predAbove_zero_of_ne_zero hi]
-
-@[simp]
-theorem predAbove_right_last : predAbove (i : Fin (n + 1)) (Fin.last (n + 1)) = last n := by
-  rw [predAbove_of_castSucc_lt _ _ (castSucc_lt_last _), pred_last]
-@[simp]
-theorem predAbove_last_castSucc {i : Fin (n + 1)} :
-    predAbove (Fin.last n) (i.castSucc) = i := by
-  rw [predAbove_of_le_castSucc _ _ ((castSucc_le_castSucc_iff).mpr (le_last _)), castPred_castSucc]
-@[simp]
-theorem predAbove_last_of_ne_last {i : Fin (n + 2)} (hi : i ≠ last (n + 1)):
-    predAbove (Fin.last n) i = castPred i hi := by
-  rw [← exists_castSucc_eq] at hi
-  rcases hi with ⟨y, rfl⟩
-  exact predAbove_last_castSucc
-theorem predAbove_last_apply :
-    predAbove (last n) i = if hi : i = Fin.last _ then last _ else i.castPred hi := by
-  split_ifs with hi
-  · rw [hi, predAbove_right_last]
-  · rw [predAbove_last_of_ne_last hi]
-#align fin.pred_above_last_apply Fin.predAbove_last_apply
-
-theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H => by
-  dsimp [predAbove]
-  split_ifs with ha hb hb
-  all_goals simp only [le_iff_val_le_val, coe_pred]
-  · exact pred_le_pred H
-  · calc
-      _ ≤ _ := Nat.pred_le _
-      _ ≤ _ := H
-  · simp at ha
-    exact le_pred_of_lt (lt_of_le_of_lt ha hb)
-  · exact H
-#align fin.pred_above_right_monotone Fin.predAbove_right_monotone
-
-theorem predAbove_left_monotone (i : Fin (n + 1)) :
-    Monotone fun p => predAbove p i := fun a b H => by
-  dsimp [predAbove]
-  split_ifs with ha hb hb
-  · rfl
-  · exact pred_le _
-  · have : b < a := castSucc_lt_castSucc_iff.mpr (hb.trans_le (le_of_not_gt ha))
-    exact absurd H this.not_le
-  · rfl
-#align fin.pred_above_left_monotone Fin.predAbove_left_monotone
-
-/-- Sending `Fin (n+1)` to `Fin n` by subtracting one from anything above `p`
-then back to `Fin (n+1)` with a gap around `p` is the identity away from `p`. -/
-@[simp]
-theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ castSucc p) :
-    p.castSucc.succAbove (p.predAbove i) = i := by
-  obtain h | h := h.lt_or_lt
-  · rw [predAbove_of_le_castSucc _ _ h.le, succAbove_castPred_of_lt _ _ h]
-  · rw [predAbove_of_castSucc_lt _ _ h, succAbove_pred_of_lt _ _ h]
-#align fin.succ_above_pred_above Fin.succAbove_predAbove
-
-/-- Sending `Fin n` into `Fin (n + 1)` with a gap at `p`
-then back to `Fin n` by subtracting one from anything above `p` is the identity. -/
-@[simp]
-theorem predAbove_succAbove (p : Fin n) (i : Fin n) :
-    p.predAbove ((castSucc p).succAbove i) = i := by
-  obtain h | h := le_or_lt p i
-  · rw [succAbove_castSucc_of_le _ _ h, predAbove_succ_of_le _ _ h]
-  · rw [succAbove_castSucc_of_lt _ _ h, predAbove_castSucc_of_le _ _ h.le]
-#align fin.pred_above_succ_above Fin.predAbove_succAbove
-
-/-- `succ` commutes with `predAbove`. -/
-@[simp]
-theorem succ_predAbove_succ {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
-    a.succ.predAbove b.succ = (a.predAbove b).succ := by
-  obtain h | h := (le_or_lt (succ a) b)
-  · rw [predAbove_of_castSucc_lt _ _ h, predAbove_succ_of_le _ _ h, succ_pred]
-  · rw [predAbove_of_lt_succ _ _ h, predAbove_succ_of_lt _ _ h, succ_castPred_eq_castPred_succ]
-#align fin.succ_pred_above_succ Fin.succ_predAbove_succ
-
-/-- `castSucc` commutes with `predAbove`. -/
-@[simp]
-theorem castSucc_predAbove_castSucc {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
-    a.castSucc.predAbove b.castSucc = (a.predAbove b).castSucc := by
-  obtain h | h := (lt_or_le (castSucc a) b)
-  · rw [predAbove_of_castSucc_lt _ _ h, predAbove_castSucc_of_lt _ _ h,
-      castSucc_pred_eq_pred_castSucc]
-  · rw [predAbove_of_le_castSucc _ _ h, predAbove_castSucc_of_le _ _ h, castSucc_castPred]
-
-/-- `rev` commutes with `predAbove`. -/
-theorem rev_predAbove {n : ℕ} (p : Fin n) (i : Fin (n + 1)) :
-    (predAbove p i).rev = predAbove p.rev i.rev := by
-  rw [predAbove_rev_left, rev_rev]
-
-end PredAbove
-
 #align fin.coe_clamp Fin.coe_clamp
 
 @[simp]
@@ -2169,17 +1660,6 @@ theorem coe_ofNat_eq_mod (m n : ℕ) [NeZero m] :
   rfl
 #align fin.coe_of_nat_eq_mod Fin.coe_ofNat_eq_mod
 
-theorem forall_fin_succ' {P : Fin (n + 1) → Prop} :
-    (∀ i, P i) ↔ (∀ i : Fin n, P i.castSucc) ∧ P (.last _) :=
-  ⟨fun H => ⟨fun _ => H _, H _⟩, fun ⟨H0, H1⟩ i => Fin.lastCases H1 H0 i⟩
-
--- to match `Fin.eq_zero_or_eq_succ`
-theorem eq_castSucc_or_eq_last {n : Nat} (i : Fin (n + 1)) :
-    (∃ j : Fin n, i = j.castSucc) ∨ i = last n := by
-  induction i using reverseInduction with
-  | last => right; rfl
-  | cast n => left; exact ⟨_, rfl⟩
-
 section Mul
 
 /-!

Rename succAbove_below, succAbove_above, predAbove_below and predAbove_Above to more appropriate things, and vary and extend these results to allow for faster proofs elsewhere.

Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -408,6 +408,18 @@ theorem rev_eq_iff {i j : Fin n} : rev i = j ↔ i = rev j := by
 
 theorem rev_ne_iff {i j : Fin n} : rev i ≠ j ↔ i ≠ rev j := rev_eq_iff.not
 
+theorem rev_lt_iff {i j : Fin n} : rev i < j ↔ rev j < i := by
+  rw [← rev_lt_rev, rev_rev]
+
+theorem rev_le_iff {i j : Fin n} : rev i ≤ j ↔ rev j ≤ i := by
+  rw [← rev_le_rev, rev_rev]
+
+theorem lt_rev_iff {i j : Fin n} : i < rev j ↔ j < rev i := by
+  rw [← rev_lt_rev, rev_rev]
+
+theorem le_rev_iff {i j : Fin n} : i ≤ rev j ↔ j ≤ rev i := by
+  rw [← rev_le_rev, rev_rev]
+
 #align fin.last Fin.last
 #align fin.coe_last Fin.val_last
 
@@ -727,6 +739,14 @@ theorem val_succEmb : ⇑(succEmb n) = Fin.succ := rfl
 #align fin.succ_le_succ_iff Fin.succ_le_succ_iff
 #align fin.succ_lt_succ_iff Fin.succ_lt_succ_iff
 
+@[simp]
+theorem exists_succ_eq {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠ 0 :=
+  ⟨fun ⟨_, hy⟩ => hy ▸ succ_ne_zero _, x.cases (fun h => h.irrefl.elim) (fun _ _ => ⟨_, rfl⟩)⟩
+#align fin.exists_succ_eq_iff Fin.exists_succ_eq
+
+theorem exists_succ_eq_of_ne_zero {x : Fin (n + 1)} (h : x ≠ 0) :
+    ∃ y, Fin.succ y = x := exists_succ_eq.mpr h
+
 theorem succ_injective (n : ℕ) : Injective (@Fin.succ n) := (succEmb n).injective
 #align fin.succ_injective Fin.succ_injective
 
@@ -955,6 +975,13 @@ theorem castSucc_lt_or_lt_succ (p : Fin (n + 1)) (i : Fin n) : castSucc i < p 
   (lt_or_le (castSucc i) p).imp id (fun h => le_castSucc_iff.mp h)
 #align fin.succ_above_lt_gt Fin.castSucc_lt_or_lt_succ
 
+theorem succ_le_or_le_castSucc (p : Fin (n + 1)) (i : Fin n) : succ i ≤ p ∨ p ≤ i.castSucc := by
+  rw [le_castSucc_iff, ← castSucc_lt_iff_succ_le]
+  exact p.castSucc_lt_or_lt_succ i
+
+theorem exists_castSucc_eq_of_ne_last {x : Fin (n + 1)} (h : x ≠ (last _)) :
+    ∃ y, Fin.castSucc y = x := exists_castSucc_eq.mpr h
+
 theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
   (castSuccEmb : Fin n ↪o _).injective
 #align fin.cast_succ_injective Fin.castSucc_injective
@@ -997,9 +1024,21 @@ theorem castSucc_ne_zero_iff' [NeZero n] (a : Fin n) : castSucc a ≠ 0 ↔ a 
   not_iff_not.mpr <| castSucc_eq_zero_iff' a
 #align fin.cast_succ_ne_zero_iff Fin.castSucc_ne_zero_iff
 
+theorem castSucc_ne_zero_of_lt {p i : Fin n} (h : p < i) : castSucc i ≠ 0 := by
+  cases n
+  · exact i.elim0
+  · rw [castSucc_ne_zero_iff']
+    exact ((zero_le _).trans_lt h).ne'
+
 theorem succ_ne_last_iff (a : Fin (n + 1)) : succ a ≠ last (n + 1) ↔ a ≠ last n :=
   not_iff_not.mpr <| succ_eq_last_succ a
 
+theorem succ_ne_last_of_lt {p i : Fin n} (h : i < p) : succ i ≠ last n := by
+  cases n
+  · exact i.elim0
+  · rw [succ_ne_last_iff]
+    exact ((le_last _).trans_lt' h).ne
+
 #align fin.cast_succ_fin_succ Fin.castSucc_fin_succ
 
 @[norm_cast, simp]
@@ -1009,6 +1048,7 @@ theorem coe_eq_castSucc {a : Fin n} : (a : Fin (n + 1)) = castSucc a := by
 #align fin.coe_eq_cast_succ Fin.coe_eq_castSucc
 
 #align fin.coe_succ_eq_succ Fin.coeSucc_eq_succ
+
 #align fin.lt_succ Fin.lt_succ
 
 @[simp]
@@ -1140,9 +1180,15 @@ theorem le_pred_iff {i : Fin (n + 1)} (hi : i ≠ 0) : j ≤ pred i hi ↔ succ
 
 theorem castSucc_pred_eq_pred_castSucc {a : Fin (n + 1)} (ha : a ≠ 0)
     (ha' := a.castSucc_ne_zero_iff.mpr ha) :
-    castSucc (a.pred ha) = (castSucc a).pred ha' := rfl
+    (a.pred ha).castSucc = (castSucc a).pred ha' := rfl
 #align fin.cast_succ_pred_eq_pred_cast_succ Fin.castSucc_pred_eq_pred_castSucc
 
+theorem castSucc_pred_add_one_eq {a : Fin (n + 1)} (ha : a ≠ 0) :
+    (a.pred ha).castSucc + 1 = a := by
+  cases' a using cases with a
+  · exact (ha rfl).elim
+  · rw [pred_succ, coeSucc_eq_succ]
+
 theorem le_pred_castSucc_iff {a b : Fin (n + 1)} (ha : castSucc a ≠ 0) :
     b ≤ (castSucc a).pred ha ↔ b < a := by
   rw [le_pred_iff, succ_le_castSucc_iff]
@@ -1261,7 +1307,13 @@ theorem rev_castPred (h : i ≠ last n) (h' := rev_ne_iff.mpr ((rev_zero _).symm
 
 theorem succ_castPred_eq_castPred_succ {a : Fin (n + 1)} (ha : a ≠ last n)
     (ha' := a.succ_ne_last_iff.mpr ha) :
-    succ (a.castPred ha) = (succ a).castPred ha' := rfl
+    (a.castPred ha).succ = (succ a).castPred ha' := rfl
+
+theorem succ_castPred_eq_add_one {a : Fin (n + 1)} (ha : a ≠ last n) :
+    (a.castPred ha).succ = a + 1 := by
+  cases' a using lastCases with a
+  · exact (ha rfl).elim
+  · rw [castPred_castSucc, coeSucc_eq_succ]
 
 theorem castpred_succ_le_iff {a b : Fin (n + 1)} (ha : succ a ≠ last (n + 1)) :
     (succ a).castPred ha ≤ b ↔ a < b := by
@@ -1601,23 +1653,78 @@ def succAbove (p : Fin (n + 1)) (i : Fin n) : Fin (n + 1) :=
 
 /-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
 embeds `i` by `castSucc` when the resulting `i.castSucc < p`. -/
-theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : castSucc i < p) :
+theorem succAbove_of_castSucc_lt (p : Fin (n + 1)) (i : Fin n) (h : castSucc i < p) :
     p.succAbove i = castSucc i := if_pos h
-#align fin.succ_above_below Fin.succAbove_below
+#align fin.succ_above_below Fin.succAbove_of_castSucc_lt
+
+theorem succAbove_of_succ_le (p : Fin (n + 1)) (i : Fin n) (h : succ i ≤ p) :
+    p.succAbove i = castSucc i :=
+  succAbove_of_castSucc_lt _ _ (castSucc_lt_iff_succ_le.mpr h)
 
 /-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
 embeds `i` by `succ` when the resulting `p < i.succ`. -/
-theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ castSucc i) :
+theorem succAbove_of_le_castSucc (p : Fin (n + 1)) (i : Fin n) (h : p ≤ castSucc i) :
     p.succAbove i = i.succ := if_neg h.not_lt
-#align fin.succ_above_above Fin.succAbove_above
+#align fin.succ_above_above Fin.succAbove_of_le_castSucc
+
+theorem succAbove_of_lt_succ (p : Fin (n + 1)) (i : Fin n) (h : p < succ i) :
+    p.succAbove i = succ i := succAbove_of_le_castSucc _ _ (le_castSucc_iff.mpr h)
+
+theorem succAbove_succ_of_lt (p i : Fin n) (h : p < i) :
+    succAbove p.succ i = i.succ := succAbove_of_lt_succ _ _ (succ_lt_succ_iff.mpr h)
+theorem succAbove_succ_of_le (p i : Fin n) (h : i ≤ p) :
+    succAbove p.succ i = i.castSucc := succAbove_of_succ_le _ _ (succ_le_succ_iff.mpr h)
+@[simp]
+theorem succAbove_succ_self (j : Fin n) : j.succ.succAbove j = j.castSucc :=
+  succAbove_succ_of_le _ _ le_rfl
+
+theorem succAbove_castSucc_of_lt (p i : Fin n) (h : i < p) :
+    succAbove p.castSucc i = i.castSucc :=
+  succAbove_of_castSucc_lt _ _ (castSucc_lt_castSucc_iff.mpr h)
+theorem succAbove_castSucc_of_le (p i : Fin n) (h : p ≤ i) :
+    succAbove p.castSucc i = i.succ :=
+  succAbove_of_le_castSucc _ _ (castSucc_le_castSucc_iff.mpr h)
+@[simp]
+theorem succAbove_castSucc_self (j : Fin n) : succAbove j.castSucc j = j.succ :=
+  succAbove_castSucc_of_le _ _ le_rfl
+
+theorem succAbove_pred_of_lt (p i : Fin (n + 1)) (h : p < i) (hi := ((zero_le p).trans_lt h).ne') :
+    succAbove p (i.pred hi) = i := by
+  rw [succAbove_of_lt_succ _ _ (succ_pred _ _ ▸ h), succ_pred]
+theorem succAbove_pred_of_le (p i : Fin (n + 1)) (h : i ≤ p) (hi : i ≠ 0):
+    succAbove p (i.pred hi) = (i.pred hi).castSucc := succAbove_of_succ_le _ _ (succ_pred _ _ ▸ h)
+@[simp]
+theorem succAbove_pred_self (p : Fin (n + 1)) (h : p ≠ 0) :
+    succAbove p (p.pred h) = (p.pred h).castSucc := succAbove_pred_of_le _ _ le_rfl h
+
+theorem succAbove_castPred_of_lt (p i : Fin (n + 1)) (h : i < p)
+    (hi := ((le_last p).trans_lt' h).ne) : succAbove p (i.castPred hi) = i := by
+  rw [succAbove_of_castSucc_lt _ _ (castSucc_castPred _ _ ▸ h), castSucc_castPred]
+theorem succAbove_castPred_of_le (p i : Fin (n + 1)) (h : p ≤ i) (hi : i ≠ last n):
+    succAbove p (i.castPred hi) = (i.castPred hi).succ :=
+  succAbove_of_le_castSucc _ _ (castSucc_castPred _ _ ▸ h)
+theorem succAbove_castPred_self (p : Fin (n + 1)) (h: p ≠ last n):
+    succAbove p (p.castPred h) = (p.castPred h).succ :=
+  succAbove_castPred_of_le _ _ le_rfl h
+
+theorem succAbove_rev_left (p : Fin (n + 1)) (i : Fin n) :
+    p.rev.succAbove i = (p.succAbove i.rev).rev := by
+  obtain h | h := (rev p).succ_le_or_le_castSucc i
+  · rw [succAbove_of_succ_le _ _ h,
+      succAbove_of_le_castSucc _ _ (rev_succ _ ▸ (le_rev_iff.mpr h)), rev_succ, rev_rev]
+  · rw [succAbove_of_le_castSucc _ _ h,
+      succAbove_of_succ_le _ _ (rev_castSucc _ ▸ (rev_le_iff.mpr h)), rev_castSucc, rev_rev]
+theorem succAbove_rev_right (p : Fin (n + 1)) (i : Fin n) :
+    p.succAbove i.rev = (p.rev.succAbove i).rev := by
+  rw [succAbove_rev_left, rev_rev]
 
 /-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
 never results in `p` itself -/
 theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p := by
   rcases p.castSucc_lt_or_lt_succ i with (h | h)
-  · rw [succAbove_below _ _ h]
+  · rw [succAbove_of_castSucc_lt _ _ h]
     exact h.ne
-  · rw [succAbove_above _ _ (le_castSucc_iff.mpr h)]
+  · rw [succAbove_of_lt_succ _ _ h]
     exact h.ne'
 #align fin.succ_above_ne Fin.succAbove_ne
 theorem ne_succAbove (p : Fin (n + 1)) (i : Fin n) : p ≠ p.succAbove i :=
@@ -1653,7 +1760,7 @@ def succAboveEmb (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
 
 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 := by
-  rw [Fin.succAbove_below]
+  rw [Fin.succAbove_of_castSucc_lt]
   · exact castSucc_zero'
   · exact bot_lt_iff_ne_bot.mpr ha
 #align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zero
@@ -1679,10 +1786,7 @@ theorem succAbove_zero_apply (i : Fin n) : succAbove 0 i = succ i := by rw [succ
 @[simp]
 theorem succAbove_ne_last_last {a : Fin (n + 2)} (h : a ≠ last (n + 1)) :
     a.succAbove (last n) = last (n + 1) := by
-  rw [succAbove_above]
-  · exact succ_last _
-  · rw [le_castSucc_iff, succ_last]
-    exact lt_top_iff_ne_top.mpr h
+  rw [succAbove_of_lt_succ _ _ (succ_last _ ▸ lt_top_iff_ne_top.mpr h), succ_last]
 
 theorem succAbove_eq_last_iff {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ last _) :
     a.succAbove b = last _ ↔ b = last _ := by
@@ -1696,7 +1800,7 @@ theorem succAbove_ne_last {a : Fin (n + 2)} {b : Fin (n + 1)}
 @[simp]
 theorem succAbove_last : succAbove (Fin.last n) = castSucc := by
   ext
-  simp only [succAbove_below, castSucc_lt_last]
+  simp only [succAbove_of_castSucc_lt, castSucc_lt_last]
 #align fin.succ_above_last Fin.succAbove_last
 
 theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = castSucc i := by
@@ -1711,67 +1815,53 @@ theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = castSucc i
 
 /-- Embedding `i : Fin n` into `Fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
-@[simp]
-theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ castSucc i < p := by
-  refine' Iff.intro _ _
-  · intro h
-    cases' lt_or_le (castSucc i) p with H H
-    · exact H
-    · rw [succAbove_above _ _ H] at h
-      exact lt_trans (castSucc_lt_succ i) h
-  · intro h
-    rw [succAbove_below _ _ h]
-    exact h
-#align fin.succ_above_lt_iff Fin.succAbove_lt_iff
+theorem succAbove_lt_iff_castSucc_lt (p : Fin (n + 1)) (i : Fin n) :
+    p.succAbove i < p ↔ castSucc i < p := by
+  cases' castSucc_lt_or_lt_succ p i with H H
+  · rwa [iff_true_right H, succAbove_of_castSucc_lt _ _ H]
+  · rw [castSucc_lt_iff_succ_le, iff_false_right H.not_le, succAbove_of_lt_succ _ _ H]
+    exact H.le.not_lt
+#align fin.succ_above_lt_iff Fin.succAbove_lt_iff_castSucc_lt
+
+theorem succAbove_lt_iff_succ_le (p : Fin (n + 1)) (i : Fin n) :
+    p.succAbove i < p ↔ succ i ≤ p := by
+  rw [succAbove_lt_iff_castSucc_lt, castSucc_lt_iff_succ_le]
 
 /-- Embedding `i : Fin n` into `Fin (n + 1)` using a pivot `p` that is lesser
 results in a value that is greater than `p`. -/
-theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p ≤ castSucc i := by
-  refine' Iff.intro _ _
-  · intro h
-    cases' lt_or_le (castSucc i) p with H H
-    · rw [succAbove_below _ _ H] at h
-      exact le_of_lt h
-    · exact H
-  · intro h
-    rw [succAbove_above _ _ h]
-    exact lt_of_le_of_lt h (castSucc_lt_succ i)
-#align fin.lt_succ_above_iff Fin.lt_succAbove_iff
+theorem lt_succAbove_iff_le_castSucc (p : Fin (n + 1)) (i : Fin n) :
+    p < p.succAbove i ↔ p ≤ castSucc i := by
+  cases' castSucc_lt_or_lt_succ p i with H H
+  · rw [iff_false_right H.not_le, succAbove_of_castSucc_lt _ _ H]
+    exact H.le.not_lt
+  · rwa [succAbove_of_lt_succ _ _ H, iff_true_left H, le_castSucc_iff]
+#align fin.lt_succ_above_iff Fin.lt_succAbove_iff_le_castSucc
+
+theorem lt_succAbove_iff_lt_castSucc (p : Fin (n + 1)) (i : Fin n) :
+    p < p.succAbove i ↔ p < succ i := by
+  rw [lt_succAbove_iff_le_castSucc, le_castSucc_iff]
 
 /-- Embedding a positive `Fin n` results in a positive `Fin (n + 1)` -/
 theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i := by
   by_cases H : castSucc i < p
-  · simpa [succAbove_below _ _ H] using castSucc_pos' h
-  · simp [succAbove_above _ _ (le_of_not_lt H)]
+  · simpa [succAbove_of_castSucc_lt _ _ H] using castSucc_pos' h
+  · simp [succAbove_of_le_castSucc _ _ (le_of_not_lt H)]
 #align fin.succ_above_pos Fin.succAbove_pos
 
-@[simp]
-theorem succAbove_castLT {x y : Fin (n + 1)} (h : x < y)
-    (hx : x.1 < n := lt_of_lt_of_le h y.le_last) : y.succAbove (x.castLT hx) = x := by
-  rw [succAbove_below, castSucc_castLT]
-  exact h
-#align fin.succ_above_cast_lt Fin.succAbove_castLT
-
-@[simp]
-theorem succAbove_pred {x y : Fin (n + 1)} (h : x < y)
-    (hy : y ≠ 0 := (x.zero_le.trans_lt h).ne') : x.succAbove (y.pred hy) = y := by
-  rw [succAbove_above, succ_pred]
-  simpa [le_iff_val_le_val] using Nat.le_sub_one_of_lt h
-#align fin.succ_above_pred Fin.succAbove_pred
-
-theorem castLT_succAbove {x : Fin n} {y : Fin (n + 1)} (h : castSucc x < y)
-    (h' : (y.succAbove x).1 < n := lt_of_lt_of_le ((succAbove_lt_iff _ _).2 h) (le_last y)) :
-    (y.succAbove x).castLT h' = x := by simp only [succAbove_below _ _ h, castLT_castSucc]
-#align fin.cast_lt_succ_above Fin.castLT_succAbove
+theorem castPred_succAbove (x : Fin n) (y : Fin (n + 1)) (h : castSucc x < y)
+    (h' := ((le_last y).trans_lt' ((succAbove_lt_iff_castSucc_lt _ _).mpr h)).ne) :
+    (y.succAbove x).castPred h' = x := by
+  rw [castPred_eq_iff_eq_castSucc, succAbove_of_castSucc_lt _ _ h]
+#align fin.cast_lt_succ_above Fin.castPred_succAbove
 
-theorem pred_succAbove {x : Fin n} {y : Fin (n + 1)} (h : y ≤ castSucc x)
-    (h' : (y.succAbove x) ≠ 0 := (y.zero_le.trans_lt <| (lt_succAbove_iff _ _).2 h).ne') :
-    (y.succAbove x).pred h' = x := by simp only [succAbove_above _ _ h, pred_succ]
+theorem pred_succAbove (x : Fin n) (y : Fin (n + 1)) (h : y ≤ castSucc x)
+    (h' := (y.zero_le.trans_lt <| (lt_succAbove_iff_le_castSucc _ _).2 h).ne') :
+    (y.succAbove x).pred h' = x := by simp only [succAbove_of_le_castSucc _ _ h, pred_succ]
 #align fin.pred_succ_above Fin.pred_succAbove
 
 theorem exists_succAbove_eq {x y : Fin (n + 1)} (h : x ≠ y) : ∃ z, y.succAbove z = x := by
   cases' h.lt_or_lt with hlt hlt
-  exacts [⟨_, succAbove_castLT hlt⟩, ⟨_, succAbove_pred hlt⟩]
+  exacts [⟨_, succAbove_castPred_of_lt _ _ hlt⟩, ⟨_, succAbove_pred_of_lt _ _ hlt⟩]
 #align fin.exists_succ_above_eq Fin.exists_succAbove_eq
 
 @[simp]
@@ -1793,11 +1883,6 @@ theorem range_succ (n : ℕ) : Set.range (Fin.succ : Fin n → Fin (n + 1)) = {0
   exact range_succAbove (0 : Fin (n + 1))
 #align fin.range_succ Fin.range_succ
 
-@[simp]
-theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠ 0 := by
-  convert @exists_succAbove_eq_iff n 0 x
-#align fin.exists_succ_eq_iff Fin.exists_succ_eq_iff
-
 /-- `succAbove` is injective at the pivot -/
 theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
   simpa [range_succAbove] using congr_arg (fun f : Fin n → Fin (n + 1) => (Set.range f)ᶜ) h
@@ -1816,18 +1901,16 @@ theorem zero_succAbove {n : ℕ} (i : Fin n) : (0 : Fin (n + 1)).succAbove i = i
 
 @[simp]
 theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : succAbove i.succ 0 = 0 :=
-  succAbove_below i.succ 0 (by simp only [castSucc_zero', succ_pos])
+  succAbove_of_castSucc_lt i.succ 0 (by simp only [castSucc_zero', succ_pos])
 #align fin.succ_succ_above_zero Fin.succ_succAbove_zero
 
 /-- `succ` commutes with `succAbove`. -/
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
     i.succ.succAbove j.succ = (i.succAbove j).succ := by
-  rcases le_or_lt i (castSucc j) with (h | h)
-  · rw [succAbove_above _ _ h,
-    succAbove_above _ _ (succ_le_castSucc_iff.mpr (le_castSucc_iff.mp h))]
-  · rw [succAbove_below _ _ h,
-    succAbove_below _ _ (castSucc_lt_succ_iff.mpr (castSucc_lt_iff_succ_le.mp h)), succ_castSucc]
+  rcases lt_or_le i (succ j) with (h | h)
+  · rw [succAbove_of_lt_succ _ _ h, succAbove_succ_of_lt _ _ h]
+  · rwa [succAbove_of_castSucc_lt _ _ h, succAbove_succ_of_le, succ_castSucc]
 #align fin.succ_succ_above_succ Fin.succ_succAbove_succ
 
 /-- `castSucc` commutes with `succAbove`. -/
@@ -1835,8 +1918,8 @@ theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
 theorem castSucc_succAbove_castSucc {n : ℕ} {i : Fin (n + 1)} {j : Fin n} :
     i.castSucc.succAbove j.castSucc = (i.succAbove j).castSucc := by
   rcases le_or_lt i (castSucc j) with (h | h)
-  · rw [succAbove_above _ _ h, succAbove_above _ _ (castSucc_le_castSucc_iff.mpr h), succ_castSucc]
-  · rw [succAbove_below _ _ h, succAbove_below _ _ (castSucc_lt_castSucc_iff.mpr h)]
+  · rw [succAbove_of_le_castSucc _ _ h, succAbove_castSucc_of_le _ _ h, succ_castSucc]
+  · rw [succAbove_of_castSucc_lt _ _ h, succAbove_castSucc_of_lt _ _ h]
 
 /-- `pred` commutes with `succAbove`. -/
 theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
@@ -1855,11 +1938,7 @@ theorem castPred_succAbove_castPred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a
 /-- `rev` commutes with `succAbove`. -/
 lemma rev_succAbove (p : Fin (n + 1)) (i : Fin n) :
     rev (succAbove p i) = succAbove (rev p) (rev i) := by
-  cases' lt_or_le (castSucc i) p with h h
-  · rw [succAbove_below _ _ h, rev_castSucc, succAbove_above]
-    rwa [← rev_succ, rev_le_rev]
-  · rw [succAbove_above _ _ h, rev_succ, succAbove_below]
-    rwa [← rev_succ, rev_lt_rev, lt_def, val_succ, Nat.lt_succ_iff]
+  rw [succAbove_rev_left, rev_rev]
 
 --@[simp] -- porting note: can be proved by `simp`
 theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 := by
@@ -1899,54 +1978,107 @@ def predAbove (p : Fin n) (i : Fin (n + 1)) : Fin n :=
   else castPred i ((le_of_not_lt h).trans_lt (castSucc_lt_last _)).ne
 #align fin.pred_above Fin.predAbove
 
-theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H => by
-  dsimp [predAbove]
-  split_ifs with ha hb hb
-  all_goals simp only [le_iff_val_le_val, coe_pred]
-  · exact pred_le_pred H
-  · calc
-      _ ≤ _ := Nat.pred_le _
-      _ ≤ _ := H
-  · simp at ha
-    exact le_pred_of_lt (lt_of_le_of_lt ha hb)
-  · exact H
-#align fin.pred_above_right_monotone Fin.predAbove_right_monotone
-
-theorem predAbove_left_monotone (i : Fin (n + 1)) :
-    Monotone fun p => predAbove p i := fun a b H => by
-  dsimp [predAbove]
-  split_ifs with ha hb hb
-  · rfl
-  · exact pred_le _
-  · have : b < a := castSucc_lt_castSucc_iff.mpr (hb.trans_le (le_of_not_gt ha))
-    exact absurd H this.not_le
-  · rfl
-#align fin.pred_above_left_monotone Fin.predAbove_left_monotone
-
-@[simp]
-theorem predAbove_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred hi := by
-  dsimp [predAbove]
-  rw [dif_pos]
-  exact pos_iff_ne_zero.mpr hi
-#align fin.pred_above_zero Fin.predAbove_zero
-
-theorem predAbove_below (p : Fin n) (i : Fin (n + 1)) (h : i ≤ castSucc p)
+theorem predAbove_of_le_castSucc (p : Fin n) (i : Fin (n + 1)) (h : i ≤ castSucc p)
     (hi := (h.trans_lt (castSucc_lt_last _)).ne) :
     p.predAbove i = i.castPred hi := dif_neg h.not_lt
-#align fin.pred_above_below Fin.predAbove_below
+#align fin.pred_above_below Fin.predAbove_of_le_castSucc
+theorem predAbove_of_lt_succ (p : Fin n) (i : Fin (n + 1)) (h : i < succ p)
+    (hi := ((le_last _).trans_lt' h).ne) :
+    p.predAbove i = i.castPred hi := predAbove_of_le_castSucc _ _ (le_castSucc_iff.mpr h)
 
-theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : castSucc p < i)
+theorem predAbove_of_castSucc_lt (p : Fin n) (i : Fin (n + 1)) (h : castSucc p < i)
     (hi := ((zero_le _).trans_lt h).ne') :
     p.predAbove i = i.pred hi := dif_pos h
-#align fin.pred_above_above Fin.predAbove_above
+#align fin.pred_above_above Fin.predAbove_of_castSucc_lt
+theorem predAbove_of_succ_le (p : Fin n) (i : Fin (n + 1)) (h : succ p ≤ i)
+    (hi := (h.trans_lt' (succ_pos _)).ne') :
+    p.predAbove i = i.pred hi := predAbove_of_castSucc_lt _ _ (castSucc_lt_iff_succ_le.mpr h)
+
+theorem predAbove_succ_of_lt (p i : Fin n) (h : i < p) (hi := succ_ne_last_of_lt h) :
+    p.predAbove (succ i) = (i.succ).castPred hi := by
+  rw [predAbove_of_lt_succ _ _ (succ_lt_succ_iff.mpr h)]
+theorem predAbove_succ_of_le (p i : Fin n) (h : p ≤ i) :
+    p.predAbove (succ i) = i := by
+  rw [predAbove_of_succ_le _ _ (succ_le_succ_iff.mpr h), pred_succ]
+@[simp]
+theorem predAbove_succ_self (p : Fin n) : p.predAbove (succ p) = p :=
+  predAbove_succ_of_le _ _ le_rfl
+
+theorem predAbove_castSucc_of_lt (p i : Fin n) (h : p < i) (hi := castSucc_ne_zero_of_lt h) :
+    p.predAbove (castSucc i) = i.castSucc.pred hi := by
+  rw [predAbove_of_castSucc_lt _ _ (castSucc_lt_castSucc_iff.mpr h)]
+theorem predAbove_castSucc_of_le (p i : Fin n) (h : i ≤ p) :
+    p.predAbove (castSucc i) = i := by
+  rw [predAbove_of_le_castSucc _ _ (castSucc_le_castSucc_iff.mpr h), castPred_castSucc]
+@[simp]
+theorem predAbove_castSucc_self (p : Fin n) : p.predAbove (castSucc p) = p :=
+  predAbove_castSucc_of_le _ _ le_rfl
+
+theorem predAbove_pred_of_lt (p i : Fin (n + 1)) (h : i < p) (hp := ((zero_le i).trans_lt h).ne')
+    (hi := ((le_last p).trans_lt' h).ne) : (pred p hp).predAbove i = castPred i hi := by
+  rw [predAbove_of_lt_succ _ _ (succ_pred _ _ ▸ h)]
+theorem predAbove_pred_of_le (p i : Fin (n + 1)) (h : p ≤ i) (hp : p ≠ 0)
+    (hi := (h.trans_lt' (pos_of_ne_zero hp)).ne') : (pred p hp).predAbove i = pred i hi := by
+  rw [predAbove_of_succ_le _ _ (succ_pred _ _ ▸ h)]
+theorem predAbove_pred_self (p : Fin (n + 1)) (hp : p ≠ 0) :
+    (pred p hp).predAbove p = pred p hp := predAbove_pred_of_le _ _ le_rfl hp
+
+theorem predAbove_castPred_of_lt (p i : Fin (n + 1)) (h : p < i)
+    (hp := ((le_last i).trans_lt' h).ne) (hi := ((zero_le p).trans_lt h).ne') :
+    (castPred p hp).predAbove i = pred i hi := by
+  rw [predAbove_of_castSucc_lt _ _ (castSucc_castPred _ _ ▸ h)]
+theorem predAbove_castPred_of_le (p i : Fin (n + 1)) (h : i ≤ p) (hp : p ≠ last n)
+    (hi := (h.trans_lt (lt_top_iff_ne_top.mpr hp)).ne) :
+    (castPred p hp).predAbove i = castPred i hi := by
+  rw [predAbove_of_le_castSucc _ _ (castSucc_castPred _ _ ▸ h)]
+theorem predAbove_castPred_self (p : Fin (n + 1)) (hp : p ≠ last n) :
+    (castPred p hp).predAbove p = castPred p hp := predAbove_castPred_of_le _ _ le_rfl hp
+
+theorem predAbove_rev_left (p : Fin n) (i : Fin (n + 1)) :
+    p.rev.predAbove i = (p.predAbove i.rev).rev := by
+  obtain h | h := (rev i).succ_le_or_le_castSucc p
+  · rw [predAbove_of_succ_le _ _ h, rev_pred,
+      predAbove_of_le_castSucc _ _ (rev_succ _ ▸ (le_rev_iff.mpr h)), castPred_inj, rev_rev]
+  · rw [predAbove_of_le_castSucc _ _ h, rev_castPred,
+      predAbove_of_succ_le _ _ (rev_castSucc _ ▸ (rev_le_iff.mpr h)), pred_inj, rev_rev]
+theorem predAbove_rev_right (p : Fin n) (i : Fin (n + 1)) :
+    p.predAbove i.rev = (p.rev.predAbove i).rev := by
+  rw [predAbove_rev_left, rev_rev]
+
+@[simp]
+theorem predAbove_right_zero [NeZero n] {i : Fin n} : predAbove (i : Fin n) 0 = 0 := by
+  cases n
+  · exact i.elim0
+  · rw [predAbove_of_le_castSucc _ _ (zero_le _), castPred_zero]
+
+@[simp]
+theorem predAbove_zero_succ [NeZero n] {i : Fin n} : predAbove 0 (i.succ) = i := by
+  rw [predAbove_succ_of_le _ _ (Fin.zero_le' _)]
+@[simp]
+theorem succ_predAbove_zero [NeZero n] {j : Fin (n + 1)} (h : j ≠ 0) :
+    succ (predAbove 0 j) = j := by
+  rcases exists_succ_eq_of_ne_zero h with ⟨k, rfl⟩
+  rw [predAbove_zero_succ]
+@[simp]
+theorem predAbove_zero_of_ne_zero [NeZero n] {i : Fin (n + 1)} (hi : i ≠ 0) :
+    predAbove 0 i = i.pred hi := by
+  rw [← exists_succ_eq] at hi
+  rcases hi with ⟨y, rfl⟩
+  exact predAbove_zero_succ
+#align fin.pred_above_zero Fin.predAbove_zero_of_ne_zero
+theorem predAbove_zero [NeZero n] :
+    predAbove (0 : Fin n) i = if hi : i = 0 then 0 else i.pred hi := by
+  split_ifs with hi
+  · rw [hi, predAbove_right_zero]
+  · rw [predAbove_zero_of_ne_zero hi]
 
 @[simp]
 theorem predAbove_right_last : predAbove (i : Fin (n + 1)) (Fin.last (n + 1)) = last n := by
-  rw [predAbove_above _ _ (castSucc_lt_last _), pred_last]
+  rw [predAbove_of_castSucc_lt _ _ (castSucc_lt_last _), pred_last]
 @[simp]
 theorem predAbove_last_castSucc {i : Fin (n + 1)} :
     predAbove (Fin.last n) (i.castSucc) = i := by
-  rw [predAbove_below _ _ ((castSucc_le_castSucc_iff).mpr (le_last _)), castPred_castSucc]
+  rw [predAbove_of_le_castSucc _ _ ((castSucc_le_castSucc_iff).mpr (le_last _)), castPred_castSucc]
 @[simp]
 theorem predAbove_last_of_ne_last {i : Fin (n + 2)} (hi : i ≠ last (n + 1)):
     predAbove (Fin.last n) i = castPred i hi := by
@@ -1960,27 +2092,38 @@ theorem predAbove_last_apply :
   · rw [predAbove_last_of_ne_last hi]
 #align fin.pred_above_last_apply Fin.predAbove_last_apply
 
+theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H => by
+  dsimp [predAbove]
+  split_ifs with ha hb hb
+  all_goals simp only [le_iff_val_le_val, coe_pred]
+  · exact pred_le_pred H
+  · calc
+      _ ≤ _ := Nat.pred_le _
+      _ ≤ _ := H
+  · simp at ha
+    exact le_pred_of_lt (lt_of_le_of_lt ha hb)
+  · exact H
+#align fin.pred_above_right_monotone Fin.predAbove_right_monotone
+
+theorem predAbove_left_monotone (i : Fin (n + 1)) :
+    Monotone fun p => predAbove p i := fun a b H => by
+  dsimp [predAbove]
+  split_ifs with ha hb hb
+  · rfl
+  · exact pred_le _
+  · have : b < a := castSucc_lt_castSucc_iff.mpr (hb.trans_le (le_of_not_gt ha))
+    exact absurd H this.not_le
+  · rfl
+#align fin.pred_above_left_monotone Fin.predAbove_left_monotone
+
 /-- Sending `Fin (n+1)` to `Fin n` by subtracting one from anything above `p`
 then back to `Fin (n+1)` with a gap around `p` is the identity away from `p`. -/
 @[simp]
 theorem succAbove_predAbove {p : Fin n} {i : Fin (n + 1)} (h : i ≠ castSucc p) :
     p.castSucc.succAbove (p.predAbove i) = i := by
-  dsimp [predAbove, succAbove]
-  rcases p with ⟨p, _⟩
-  rcases i with ⟨i, _⟩
-  cases' lt_or_le i p with H H
-  · rw [dif_neg]
-    rw [if_pos]
-    rfl
-    exact H
-    simp only [castSucc_mk, mk_lt_mk, not_lt]
-    apply le_of_lt H
-  · rw [dif_pos]
-    rw [if_neg]
-    · simp
-    · simp only [pred, Fin.mk_lt_mk, not_lt]
-      exact Nat.le_sub_one_of_lt (h.symm.lt_of_le H)
-    · exact lt_of_le_of_ne H h.symm
+  obtain h | h := h.lt_or_lt
+  · rw [predAbove_of_le_castSucc _ _ h.le, succAbove_castPred_of_lt _ _ h]
+  · rw [predAbove_of_castSucc_lt _ _ h, succAbove_pred_of_lt _ _ h]
 #align fin.succ_above_pred_above Fin.succAbove_predAbove
 
 /-- Sending `Fin n` into `Fin (n + 1)` with a gap at `p`
@@ -1988,29 +2131,18 @@ then back to `Fin n` by subtracting one from anything above `p` is the identity.
 @[simp]
 theorem predAbove_succAbove (p : Fin n) (i : Fin n) :
     p.predAbove ((castSucc p).succAbove i) = i := by
-  dsimp [predAbove, succAbove]
-  rcases p with ⟨p, _⟩
-  rcases i with ⟨i, _⟩
-  dsimp
-  split_ifs with h₁ h₂ h₃
-  · simp only [← val_fin_lt, not_lt] at h₁ h₂
-    exact (Nat.lt_le_asymm h₁ (le_of_lt h₂)).elim
-  · rfl
-  · rfl
-  · simp only [← val_fin_lt, not_lt] at h₁ h₃
-    contradiction
+  obtain h | h := le_or_lt p i
+  · rw [succAbove_castSucc_of_le _ _ h, predAbove_succ_of_le _ _ h]
+  · rw [succAbove_castSucc_of_lt _ _ h, predAbove_castSucc_of_le _ _ h.le]
 #align fin.pred_above_succ_above Fin.predAbove_succAbove
 
 /-- `succ` commutes with `predAbove`. -/
 @[simp]
 theorem succ_predAbove_succ {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
     a.succ.predAbove b.succ = (a.predAbove b).succ := by
-  obtain h | h := (lt_or_le (castSucc a) b)
-  · rw [Fin.predAbove_above _ _ h, succ_pred,
-    Fin.predAbove_above _ _ (castSucc_lt_succ_iff.mpr (castSucc_lt_iff_succ_le.mp h)), pred_succ]
-  · rw [Fin.predAbove_below _ _ h,
-    Fin.predAbove_below _ _ (succ_le_castSucc_iff.mpr (le_castSucc_iff.mp h)),
-    succ_castPred_eq_castPred_succ]
+  obtain h | h := (le_or_lt (succ a) b)
+  · rw [predAbove_of_castSucc_lt _ _ h, predAbove_succ_of_le _ _ h, succ_pred]
+  · rw [predAbove_of_lt_succ _ _ h, predAbove_succ_of_lt _ _ h, succ_castPred_eq_castPred_succ]
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ
 
 /-- `castSucc` commutes with `predAbove`. -/
@@ -2018,19 +2150,14 @@ theorem succ_predAbove_succ {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
 theorem castSucc_predAbove_castSucc {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
     a.castSucc.predAbove b.castSucc = (a.predAbove b).castSucc := by
   obtain h | h := (lt_or_le (castSucc a) b)
-  · rw [Fin.predAbove_above _ _ h, Fin.predAbove_above _ _ (castSucc_lt_castSucc_iff.mpr h),
-    castSucc_pred_eq_pred_castSucc]
-  · rw [Fin.predAbove_below _ _ h, castSucc_castPred,
-    Fin.predAbove_below _ _ (castSucc_le_castSucc_iff.mpr h), castPred_castSucc]
+  · rw [predAbove_of_castSucc_lt _ _ h, predAbove_castSucc_of_lt _ _ h,
+      castSucc_pred_eq_pred_castSucc]
+  · rw [predAbove_of_le_castSucc _ _ h, predAbove_castSucc_of_le _ _ h, castSucc_castPred]
 
 /-- `rev` commutes with `predAbove`. -/
 theorem rev_predAbove {n : ℕ} (p : Fin n) (i : Fin (n + 1)) :
     (predAbove p i).rev = predAbove p.rev i.rev := by
-  rcases lt_or_le (castSucc p) i with (h | h)
-  · rw [predAbove_above _ _ h, rev_pred,
-    predAbove_below _ _ (by rwa [← rev_succ, rev_le_rev, ← castSucc_lt_iff_succ_le])]
-  · rw [predAbove_below _ _ h, rev_castPred,
-    predAbove_above _ _ (by rwa [← rev_succ, rev_lt_rev, ← le_castSucc_iff])]
+  rw [predAbove_rev_left, rev_rev]
 
 end PredAbove
 

There's an exciting linter failure on bump/v4.6.0, and I'm wondering if this is caused by strange simp lemmas in leanprover/std4#558, so I'm updating to that before the bump.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -209,8 +209,6 @@ section Order
 #align fin.is_le Fin.is_le
 #align fin.is_le' Fin.is_le'
 
-theorem lt_iff_val_lt_val {a b : Fin n} : a < b ↔ (a : ℕ) < b :=
-  Iff.rfl
 #align fin.lt_iff_coe_lt_coe Fin.lt_iff_val_lt_val
 
 theorem le_iff_val_le_val {a b : Fin n} : a ≤ b ↔ (a : ℕ) ≤ b :=

Refines and extends results relating to the monotonicity of succ, castSucc, and related functions

@@ -49,7 +49,7 @@ This file expands on the development in the core library.
 * `Fin.orderIsoSubtype` : coercion to `{ i // i < n }` as an `OrderIso`;
 * `Fin.valEmbedding` : coercion to natural numbers as an `Embedding`;
 * `Fin.valOrderEmbedding` : coercion to natural numbers as an `OrderEmbedding`;
-* `Fin.succEmbedding` : `Fin.succ` as an `OrderEmbedding`;
+* `Fin.succEmb` : `Fin.succ` as an `OrderEmbedding`;
 * `Fin.castLEEmb h` : `Fin.castLE` as an `OrderEmbedding`, embed `Fin n` into `Fin m`, `h : n ≤ m`;
 * `Fin.castIso` : `Fin.cast` as an `OrderIso`, order isomorphism between `Fin n` and `Fin m`
   provided that `n = m`, see also `Equiv.finCongr`;
@@ -716,21 +716,20 @@ section Succ
 #align fin.coe_succ Fin.val_succ
 #align fin.succ_pos Fin.succ_pos
 
+lemma strictMono_succ {n : ℕ} : StrictMono (succ : Fin n → Fin (n + 1)) := fun _ _ => succ_lt_succ
+
 /-- `Fin.succ` as an `OrderEmbedding` -/
-def succEmbedding (n : ℕ) : Fin n ↪o Fin (n + 1) :=
-  (OrderEmbedding.ofStrictMono Fin.succ) fun _ _ h => succ_lt_succ h
-#align fin.succ_embedding Fin.succEmbedding
+def succEmb (n : ℕ) : Fin n ↪o Fin (n + 1) := OrderEmbedding.ofStrictMono succ strictMono_succ
+#align fin.succ_embedding Fin.succEmb
 
 @[simp]
-theorem val_succEmbedding : ⇑(succEmbedding n) = Fin.succ :=
-  rfl
-#align fin.coe_succ_embedding Fin.val_succEmbedding
+theorem val_succEmb : ⇑(succEmb n) = Fin.succ := rfl
+#align fin.coe_succ_embedding Fin.val_succEmb
 
 #align fin.succ_le_succ_iff Fin.succ_le_succ_iff
 #align fin.succ_lt_succ_iff Fin.succ_lt_succ_iff
 
-theorem succ_injective (n : ℕ) : Injective (@Fin.succ n) :=
-  (succEmbedding n).injective
+theorem succ_injective (n : ℕ) : Injective (@Fin.succ n) := (succEmb n).injective
 #align fin.succ_injective Fin.succ_injective
 
 #align fin.succ_inj Fin.succ_inj
@@ -1114,6 +1113,14 @@ section Pred
 #align fin.add_nat_sub_nat Fin.addNat_subNat
 #align fin.sub_nat_add_nat Fin.subNat_addNat
 
+theorem strictMono_pred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ 0)
+    (hf₂ : StrictMono f) : StrictMono (fun a => pred (f a) (hf a)) :=
+    fun _ _ h => pred_lt_pred_iff.2 (hf₂ h)
+
+theorem monotone_pred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ 0)
+    (hf₂ : Monotone f) : Monotone (fun a => pred (f a) (hf a)) :=
+    fun _ _ h => pred_le_pred_iff.2 (hf₂ h)
+
 #align fin.nat_add_sub_nat_cast Fin.natAdd_subNat_castₓ
 
 theorem pred_one' [NeZero n] (h := (zero_ne_one' (n := n)).symm):
@@ -1142,19 +1149,23 @@ theorem le_pred_castSucc_iff {a b : Fin (n + 1)} (ha : castSucc a ≠ 0) :
     b ≤ (castSucc a).pred ha ↔ b < a := by
   rw [le_pred_iff, succ_le_castSucc_iff]
 
+theorem pred_castSucc_lt_iff {a b : Fin (n + 1)} (ha : castSucc a ≠ 0) :
+    (castSucc a).pred ha < b ↔ a ≤ b := by
+  rw [pred_lt_iff, castSucc_lt_succ_iff]
+
 theorem pred_castSucc_lt {a : Fin (n + 1)} (ha : castSucc a ≠ 0) :
-    (castSucc a).pred ha < a := by
-  rw [pred_lt_iff]
-  exact castSucc_lt_succ _
+    (castSucc a).pred ha < a := by rw [pred_castSucc_lt_iff]
 
 theorem le_castSucc_pred_iff {a b : Fin (n + 1)} (ha : a ≠ 0) :
     b ≤ castSucc (a.pred ha) ↔ b < a := by
   rw [castSucc_pred_eq_pred_castSucc, le_pred_castSucc_iff]
 
+theorem castSucc_pred_lt_iff {a b : Fin (n + 1)} (ha : a ≠ 0) :
+    castSucc (a.pred ha) < b ↔ a ≤ b := by
+  rw [castSucc_pred_eq_pred_castSucc, pred_castSucc_lt_iff]
+
 theorem castSucc_pred_lt {a : Fin (n + 1)} (ha : a ≠ 0) :
-    castSucc (a.pred ha) < a := by
-  rw [lt_iff_not_le, le_castSucc_pred_iff]
-  exact lt_irrefl _
+    castSucc (a.pred ha) < a := by rw [castSucc_pred_lt_iff]
 
 end Pred
 
@@ -1200,6 +1211,14 @@ theorem castPred_le_castPred_iff {i j : Fin (n + 1)} {hi : i ≠ last n} {hj : j
 theorem castPred_lt_castPred_iff {i j : Fin (n + 1)} {hi : i ≠ last n} {hj : j ≠ last n} :
     castPred i hi < castPred j hj ↔ i < j := Iff.rfl
 
+theorem strictMono_castPred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ last n)
+    (hf₂ : StrictMono f) : StrictMono (fun a => castPred (f a) (hf a)) :=
+    fun _ _ h => castPred_lt_castPred_iff.2 (hf₂ h)
+
+theorem monotone_castPred_comp [Preorder α] {f : α → Fin (n + 1)} (hf : ∀ a, f a ≠ last n)
+    (hf₂ : Monotone f) : Monotone (fun a => castPred (f a) (hf a)) :=
+    fun _ _ h => castPred_le_castPred_iff.2 (hf₂ h)
+
 theorem castPred_lt_iff {i : Fin (n + 1)} (hi : i ≠ last n) :
     castPred i hi < j ↔ i < castSucc j := by
   rw [← castSucc_lt_castSucc_iff, castSucc_castPred]
@@ -1234,9 +1253,6 @@ theorem castPred_one [NeZero n] (h := one_lt_last.ne) : castPred (1 : Fin (n + 2
   · rfl
 #align fin.cast_pred_one Fin.castPred_one
 
-theorem pred_lt_castPred (h₁ : i ≠ 0) (h₂ : i ≠ last n) : pred i h₁ < castPred i h₂ := by
-  rw [← castSucc_lt_castSucc_iff, castSucc_castPred, castSucc_lt_iff_succ_le, succ_pred]
-
 theorem rev_pred (h : i ≠ 0) (h' := rev_ne_iff.mpr ((rev_last _).symm ▸ h)) :
     rev (pred i h) = castPred (rev i) h' := by
   rw [← castSucc_inj, castSucc_castPred, ← rev_succ, succ_pred]
@@ -1249,23 +1265,38 @@ theorem succ_castPred_eq_castPred_succ {a : Fin (n + 1)} (ha : a ≠ last n)
     (ha' := a.succ_ne_last_iff.mpr ha) :
     succ (a.castPred ha) = (succ a).castPred ha' := rfl
 
-theorem le_castPred_succ_iff {a b : Fin (n + 1)} (ha : succ a ≠ last (n + 1)) :
+theorem castpred_succ_le_iff {a b : Fin (n + 1)} (ha : succ a ≠ last (n + 1)) :
     (succ a).castPred ha ≤ b ↔ a < b := by
   rw [castPred_le_iff, succ_le_castSucc_iff]
 
+theorem lt_castPred_succ_iff {a b : Fin (n + 1)} (ha : succ a ≠ last (n + 1)) :
+    b < (succ a).castPred ha ↔ b ≤ a := by
+  rw [lt_castPred_iff, castSucc_lt_succ_iff]
+
 theorem lt_castPred_succ {a : Fin (n + 1)} (ha : succ a ≠ last (n + 1)) :
-    a < (succ a).castPred ha := by
-  rw [lt_castPred_iff]
-  exact castSucc_lt_succ _
+    a < (succ a).castPred ha := by rw [lt_castPred_succ_iff]
 
 theorem succ_castPred_le_iff {a b : Fin (n + 1)} (ha : a ≠ last n) :
     succ (a.castPred ha) ≤ b ↔ a < b := by
-  rw [succ_castPred_eq_castPred_succ ha, le_castPred_succ_iff]
+  rw [succ_castPred_eq_castPred_succ ha, castpred_succ_le_iff]
+
+theorem lt_succ_castPred_iff {a b : Fin (n + 1)} (ha : a ≠ last n) :
+    b < succ (a.castPred ha) ↔ b ≤ a := by
+  rw [succ_castPred_eq_castPred_succ ha, lt_castPred_succ_iff]
 
 theorem lt_succ_castPred {a : Fin (n + 1)} (ha : a ≠ last n) :
-    a < succ (a.castPred ha) := by
-  rw [lt_iff_not_le, succ_castPred_le_iff]
-  exact lt_irrefl _
+    a < succ (a.castPred ha) := by rw [lt_succ_castPred_iff]
+
+theorem castPred_le_pred_iff {a b : Fin (n + 1)} (ha : a ≠ last n) (hb : b ≠ 0) :
+    castPred a ha ≤ pred b hb ↔ a < b := by
+  rw [le_pred_iff, succ_castPred_le_iff]
+
+theorem pred_lt_castPred_iff {a b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ last n) :
+    pred a ha < castPred b hb ↔ a ≤ b := by
+  rw [lt_castPred_iff, castSucc_pred_lt_iff ha]
+
+theorem pred_lt_castPred (h₁ : a ≠ 0) (h₂ : a ≠ last n) : pred a h₁ < castPred a h₂ := by
+  rw [pred_lt_castPred_iff]
 
 end CastPred
 
@@ -1570,29 +1601,6 @@ section SuccAbove
 def succAbove (p : Fin (n + 1)) (i : Fin n) : Fin (n + 1) :=
   if castSucc i < p then i.castSucc else i.succ
 
-theorem strictMono_succAbove (p : Fin (n + 1)) : StrictMono (succAbove p) :=
-  (castSuccEmb : Fin n ↪o _).strictMono.ite (succEmbedding n).strictMono
-    (fun _ _ hij hj => lt_trans ((castSuccEmb : Fin n ↪o _).lt_iff_lt.2 hij) hj) fun i =>
-    (castSucc_lt_succ i).le
-#align fin.succ_above_aux Fin.strictMono_succAbove
-
-/--  `Fin.succAbove` as an `OrderEmbedding`, `succAboveEmb p i` embeds `Fin n` into `Fin (n + 1)`
-with a hole around `p`. -/
-@[simps! apply toEmbedding]
-def succAboveEmb (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
-  OrderEmbedding.ofStrictMono (succAbove p) (strictMono_succAbove p)
-#align fin.succ_above Fin.succAboveEmb
-
-/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
-theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
-  (strictMono_succAbove x).injective
-#align fin.succ_above_right_injective Fin.succAbove_right_injective
-
-/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
-theorem succAbove_right_inj (x : Fin (n + 1)) : x.succAbove a = x.succAbove b ↔ a = b :=
-  succAbove_right_injective.eq_iff
-#align fin.succ_above_right_inj Fin.succAbove_right_inj
-
 /-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
 embeds `i` by `castSucc` when the resulting `i.castSucc < p`. -/
 theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : castSucc i < p) :
@@ -1617,6 +1625,34 @@ theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p := by
 theorem ne_succAbove (p : Fin (n + 1)) (i : Fin n) : p ≠ p.succAbove i :=
 (succAbove_ne _ _).symm
 
+theorem strictMono_succAbove (p : Fin (n + 1)) : StrictMono (succAbove p) :=
+  strictMono_castSucc.ite strictMono_succ
+    (fun _ _ hij hj => (castSucc_lt_castSucc_iff.mpr hij).trans hj) fun i =>
+    (castSucc_lt_succ i).le
+#align fin.succ_above_aux Fin.strictMono_succAbove
+
+/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
+theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
+  (strictMono_succAbove x).injective
+#align fin.succ_above_right_injective Fin.succAbove_right_injective
+
+/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
+theorem succAbove_right_inj (x : Fin (n + 1)) : x.succAbove a = x.succAbove b ↔ a = b :=
+  succAbove_right_injective.eq_iff
+#align fin.succ_above_right_inj Fin.succAbove_right_inj
+
+theorem succAbove_lt_succAbove_iff (p : Fin (n + 1)) :
+    succAbove p i < succAbove p j ↔ i < j := (strictMono_succAbove p).lt_iff_lt
+theorem succAbove_le_succAbove_iff (p : Fin (n + 1)) :
+    succAbove p i ≤ succAbove p j ↔ i ≤ j := (strictMono_succAbove p).le_iff_le
+
+/--  `Fin.succAbove` as an `OrderEmbedding`, `succAboveEmb p i` embeds `Fin n` into `Fin (n + 1)`
+with a hole around `p`. -/
+@[simps! apply toEmbedding]
+def succAboveEmb (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
+  OrderEmbedding.ofStrictMono (succAbove p) (strictMono_succAbove p)
+#align fin.succ_above Fin.succAboveEmb
+
 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 := by
   rw [Fin.succAbove_below]

Adds lemma that shows that succAbove and castSucc commute and similar for predAbove. Perform necessary updates and refactors to get there.

@@ -1583,22 +1583,50 @@ def succAboveEmb (p : Fin (n + 1)) : Fin n ↪o Fin (n + 1) :=
   OrderEmbedding.ofStrictMono (succAbove p) (strictMono_succAbove p)
 #align fin.succ_above Fin.succAboveEmb
 
+/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
+theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
+  (strictMono_succAbove x).injective
+#align fin.succ_above_right_injective Fin.succAbove_right_injective
+
+/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
+theorem succAbove_right_inj (x : Fin (n + 1)) : x.succAbove a = x.succAbove b ↔ a = b :=
+  succAbove_right_injective.eq_iff
+#align fin.succ_above_right_inj Fin.succAbove_right_inj
+
 /-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
 embeds `i` by `castSucc` when the resulting `i.castSucc < p`. -/
 theorem succAbove_below (p : Fin (n + 1)) (i : Fin n) (h : castSucc i < p) :
     p.succAbove i = castSucc i := if_pos h
 #align fin.succ_above_below Fin.succAbove_below
 
+/-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
+embeds `i` by `succ` when the resulting `p < i.succ`. -/
+theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ castSucc i) :
+    p.succAbove i = i.succ := if_neg h.not_lt
+#align fin.succ_above_above Fin.succAbove_above
+
+/-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
+never results in `p` itself -/
+theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p := by
+  rcases p.castSucc_lt_or_lt_succ i with (h | h)
+  · rw [succAbove_below _ _ h]
+    exact h.ne
+  · rw [succAbove_above _ _ (le_castSucc_iff.mpr h)]
+    exact h.ne'
+#align fin.succ_above_ne Fin.succAbove_ne
+theorem ne_succAbove (p : Fin (n + 1)) (i : Fin n) : p ≠ p.succAbove i :=
+(succAbove_ne _ _).symm
+
 @[simp]
 theorem succAbove_ne_zero_zero [NeZero n] {a : Fin (n + 1)} (ha : a ≠ 0) : a.succAbove 0 = 0 := by
   rw [Fin.succAbove_below]
-  · simp
+  · exact castSucc_zero'
   · exact bot_lt_iff_ne_bot.mpr ha
 #align fin.succ_above_ne_zero_zero Fin.succAbove_ne_zero_zero
 
 theorem succAbove_eq_zero_iff [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) :
     a.succAbove b = 0 ↔ b = 0 := by
-  simp only [← succAbove_ne_zero_zero ha, ← succAboveEmb_apply, OrderEmbedding.eq_iff_eq, iff_self]
+  rw [← succAbove_ne_zero_zero ha, succAbove_right_inj]
 #align fin.succ_above_eq_zero_iff Fin.succAbove_eq_zero_iff
 
 theorem succAbove_ne_zero [NeZero n] {a : Fin (n + 1)} {b : Fin n} (ha : a ≠ 0) (hb : b ≠ 0) :
@@ -1612,6 +1640,24 @@ theorem succAbove_zero : succAbove (0 : Fin (n + 1)) = Fin.succ :=
   rfl
 #align fin.succ_above_zero Fin.succAbove_zero
 
+theorem succAbove_zero_apply (i : Fin n) : succAbove 0 i = succ i := by rw [succAbove_zero]
+
+@[simp]
+theorem succAbove_ne_last_last {a : Fin (n + 2)} (h : a ≠ last (n + 1)) :
+    a.succAbove (last n) = last (n + 1) := by
+  rw [succAbove_above]
+  · exact succ_last _
+  · rw [le_castSucc_iff, succ_last]
+    exact lt_top_iff_ne_top.mpr h
+
+theorem succAbove_eq_last_iff {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ last _) :
+    a.succAbove b = last _ ↔ b = last _ := by
+  simp [← succAbove_ne_last_last ha, succAbove_right_inj]
+
+theorem succAbove_ne_last {a : Fin (n + 2)} {b : Fin (n + 1)}
+    (ha : a ≠ last _) (hb : b ≠ last _) : a.succAbove b ≠ last _ :=
+  mt (succAbove_eq_last_iff ha).mp hb
+
 /-- Embedding `Fin n` into `Fin (n + 1)` with a hole around `last n` embeds by `castSucc`. -/
 @[simp]
 theorem succAbove_last : succAbove (Fin.last n) = castSucc := by
@@ -1623,15 +1669,8 @@ theorem succAbove_last_apply (i : Fin n) : succAbove (Fin.last n) i = castSucc i
   rw [succAbove_last]
 #align fin.succ_above_last_apply Fin.succAbove_last_apply
 
-/-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
-embeds `i` by `succ` when the resulting `p < i.succ`. -/
-theorem succAbove_above (p : Fin (n + 1)) (i : Fin n) (h : p ≤ castSucc i) :
-    p.succAbove i = i.succ := if_neg h.not_lt
-#align fin.succ_above_above Fin.succAbove_above
-
-/-- Embedding `i : Fin n` into `Fin (n + 1)` is always about some hole `p`. -/
-theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : castSucc i < p ∨ p ≤ castSucc i :=
-  lt_or_ge (castSucc i) p
+@[deprecated] theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) :
+    castSucc i < p ∨ p ≤ castSucc i := lt_or_ge (castSucc i) p
 #align fin.succ_above_lt_ge Fin.succAbove_lt_ge
 
 @[deprecated castSucc_lt_or_lt_succ] alias succAbove_lt_gt := castSucc_lt_or_lt_succ
@@ -1642,7 +1681,7 @@ results in a value that is less than `p`. -/
 theorem succAbove_lt_iff (p : Fin (n + 1)) (i : Fin n) : p.succAbove i < p ↔ castSucc i < p := by
   refine' Iff.intro _ _
   · intro h
-    cases' succAbove_lt_ge p i with H H
+    cases' lt_or_le (castSucc i) p with H H
     · exact H
     · rw [succAbove_above _ _ H] at h
       exact lt_trans (castSucc_lt_succ i) h
@@ -1656,7 +1695,7 @@ results in a value that is greater than `p`. -/
 theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p ≤ castSucc i := by
   refine' Iff.intro _ _
   · intro h
-    cases' succAbove_lt_ge p i with H H
+    cases' lt_or_le (castSucc i) p with H H
     · rw [succAbove_below _ _ H] at h
       exact le_of_lt h
     · exact H
@@ -1665,15 +1704,6 @@ theorem lt_succAbove_iff (p : Fin (n + 1)) (i : Fin n) : p < p.succAbove i ↔ p
     exact lt_of_le_of_lt h (castSucc_lt_succ i)
 #align fin.lt_succ_above_iff Fin.lt_succAbove_iff
 
-/-- Embedding `i : Fin n` into `Fin (n + 1)` with a hole around `p : Fin (n + 1)`
-never results in `p` itself -/
-theorem succAbove_ne (p : Fin (n + 1)) (i : Fin n) : p.succAbove i ≠ p := by
-  intro eq
-  by_cases H : castSucc i < p
-  · simp [lt_irrefl, ← succAbove_below _ _ H, eq] at H
-  · simpa [← succAbove_above _ _ (le_of_not_lt H), eq, H] using castSucc_lt_succ i
-#align fin.succ_above_ne Fin.succAbove_ne
-
 /-- Embedding a positive `Fin n` results in a positive `Fin (n + 1)` -/
 theorem succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i := by
   by_cases H : castSucc i < p
@@ -1734,16 +1764,6 @@ theorem exists_succ_eq_iff {x : Fin (n + 1)} : (∃ y, Fin.succ y = x) ↔ x ≠
   convert @exists_succAbove_eq_iff n 0 x
 #align fin.exists_succ_eq_iff Fin.exists_succ_eq_iff
 
-/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
-theorem succAbove_right_injective {x : Fin (n + 1)} : Injective (succAbove x) :=
-  (succAboveEmb x).injective
-#align fin.succ_above_right_injective Fin.succAbove_right_injective
-
-/-- Given a fixed pivot `x : Fin (n + 1)`, `x.succAbove` is injective -/
-theorem succAbove_right_inj {x : Fin (n + 1)} : x.succAbove a = x.succAbove b ↔ a = b :=
-  succAbove_right_injective.eq_iff
-#align fin.succ_above_right_inj Fin.succAbove_right_inj
-
 /-- `succAbove` is injective at the pivot -/
 theorem succAbove_left_injective : Injective (@succAbove n) := fun _ _ h => by
   simpa [range_succAbove] using congr_arg (fun f : Fin n → Fin (n + 1) => (Set.range f)ᶜ) h
@@ -1765,20 +1785,48 @@ theorem succ_succAbove_zero {n : ℕ} [NeZero n] (i : Fin n) : succAbove i.succ
   succAbove_below i.succ 0 (by simp only [castSucc_zero', succ_pos])
 #align fin.succ_succ_above_zero Fin.succ_succAbove_zero
 
+/-- `succ` commutes with `succAbove`. -/
 @[simp]
 theorem succ_succAbove_succ {n : ℕ} (i : Fin (n + 1)) (j : Fin n) :
-    i.succ.succAbove j.succ = (i.succAbove j).succ :=
-  (lt_or_ge (castSucc j) i).elim
-    (fun h => by
-      have h' : castSucc j.succ < i.succ := by simpa [lt_iff_val_lt_val] using h
-      ext
-      simp [succAbove_below _ _ h, succAbove_below _ _ h'])
-    fun h => by
-    have h' : i.succ ≤ castSucc j.succ := by simpa [le_iff_val_le_val] using h
-    ext
-    simp [succAbove_above _ _ h, succAbove_above _ _ h']
+    i.succ.succAbove j.succ = (i.succAbove j).succ := by
+  rcases le_or_lt i (castSucc j) with (h | h)
+  · rw [succAbove_above _ _ h,
+    succAbove_above _ _ (succ_le_castSucc_iff.mpr (le_castSucc_iff.mp h))]
+  · rw [succAbove_below _ _ h,
+    succAbove_below _ _ (castSucc_lt_succ_iff.mpr (castSucc_lt_iff_succ_le.mp h)), succ_castSucc]
 #align fin.succ_succ_above_succ Fin.succ_succAbove_succ
 
+/-- `castSucc` commutes with `succAbove`. -/
+@[simp]
+theorem castSucc_succAbove_castSucc {n : ℕ} {i : Fin (n + 1)} {j : Fin n} :
+    i.castSucc.succAbove j.castSucc = (i.succAbove j).castSucc := by
+  rcases le_or_lt i (castSucc j) with (h | h)
+  · rw [succAbove_above _ _ h, succAbove_above _ _ (castSucc_le_castSucc_iff.mpr h), succ_castSucc]
+  · rw [succAbove_below _ _ h, succAbove_below _ _ (castSucc_lt_castSucc_iff.mpr h)]
+
+/-- `pred` commutes with `succAbove`. -/
+theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
+    (hk := succAbove_ne_zero ha hb) :
+    (a.pred ha).succAbove (b.pred hb) = (a.succAbove b).pred hk := by
+  simp_rw [← succ_inj (b := pred (succAbove a b) hk), ← succ_succAbove_succ, succ_pred]
+#align fin.pred_succ_above_pred Fin.pred_succAbove_pred
+
+/-- `castPred` commutes with `succAbove`. -/
+theorem castPred_succAbove_castPred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ last (n + 1))
+    (hb : b ≠ last n) (hk := succAbove_ne_last ha hb) :
+    (a.castPred ha).succAbove (b.castPred hb) = (a.succAbove b).castPred hk := by
+  simp_rw [← castSucc_inj (b := (a.succAbove b).castPred hk), ← castSucc_succAbove_castSucc,
+    castSucc_castPred]
+
+/-- `rev` commutes with `succAbove`. -/
+lemma rev_succAbove (p : Fin (n + 1)) (i : Fin n) :
+    rev (succAbove p i) = succAbove (rev p) (rev i) := by
+  cases' lt_or_le (castSucc i) p with h h
+  · rw [succAbove_below _ _ h, rev_castSucc, succAbove_above]
+    rwa [← rev_succ, rev_le_rev]
+  · rw [succAbove_above _ _ h, rev_succ, succAbove_below]
+    rwa [← rev_succ, rev_lt_rev, lt_def, val_succ, Nat.lt_succ_iff]
+
 --@[simp] -- porting note: can be proved by `simp`
 theorem one_succAbove_zero {n : ℕ} : (1 : Fin (n + 2)).succAbove 0 = 0 := by
   rfl
@@ -1807,14 +1855,6 @@ theorem one_succAbove_one {n : ℕ} : (1 : Fin (n + 3)).succAbove 1 = 2 := by
   exact this
 #align fin.one_succ_above_one Fin.one_succAbove_one
 
-lemma rev_succAbove (p : Fin (n + 1)) (i : Fin n) :
-    rev (succAbove p i) = succAbove (rev p) (rev i) := by
-  cases' lt_or_le (castSucc i) p with h h
-  · rw [succAbove_below _ _ h, rev_castSucc, succAbove_above]
-    rwa [← rev_succ, rev_le_rev]
-  · rw [succAbove_above _ _ h, rev_succ, succAbove_below]
-    rwa [← rev_succ, rev_lt_rev, lt_def, val_succ, Nat.lt_succ_iff]
-
 end SuccAbove
 
 section PredAbove
@@ -1927,31 +1967,37 @@ theorem predAbove_succAbove (p : Fin n) (i : Fin n) :
     contradiction
 #align fin.pred_above_succ_above Fin.predAbove_succAbove
 
-/-- `pred` commutes with `succAbove`. -/
-theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (hb : b ≠ 0)
-    (hk := succAbove_ne_zero ha hb) :
-    (a.pred ha).succAbove (b.pred hb) = (a.succAbove b).pred hk := by
-  obtain hbelow | habove := lt_or_le (castSucc b) a
-  · rw [Fin.succAbove_below]
-    · rwa [castSucc_pred_eq_pred_castSucc, Fin.pred_inj, Fin.succAbove_below]
-    · rwa [castSucc_pred_eq_pred_castSucc, pred_lt_pred_iff]
-  · rw [Fin.succAbove_above]
-    have : (b.pred hb).succ = b.succ.pred (succ_ne_zero _) := by rw [succ_pred, pred_succ]
-    · rwa [this, Fin.pred_inj, Fin.succAbove_above]
-    · rwa [castSucc_pred_eq_pred_castSucc, Fin.pred_le_pred_iff]
-#align fin.pred_succ_above_pred Fin.pred_succAbove_pred
-
 /-- `succ` commutes with `predAbove`. -/
 @[simp]
 theorem succ_predAbove_succ {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
     a.succ.predAbove b.succ = (a.predAbove b).succ := by
   obtain h | h := (lt_or_le (castSucc a) b)
-  · rw [Fin.predAbove_above _ _ h, succ_pred, Fin.predAbove_above, pred_succ]
-    rwa [castSucc_lt_succ_iff, ← castSucc_lt_iff_succ_le]
-  · rw [Fin.predAbove_below _ _ h, Fin.predAbove_below, succ_castPred_eq_castPred_succ]
-    rwa [succ_le_castSucc_iff, ← le_castSucc_iff]
+  · rw [Fin.predAbove_above _ _ h, succ_pred,
+    Fin.predAbove_above _ _ (castSucc_lt_succ_iff.mpr (castSucc_lt_iff_succ_le.mp h)), pred_succ]
+  · rw [Fin.predAbove_below _ _ h,
+    Fin.predAbove_below _ _ (succ_le_castSucc_iff.mpr (le_castSucc_iff.mp h)),
+    succ_castPred_eq_castPred_succ]
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ
 
+/-- `castSucc` commutes with `predAbove`. -/
+@[simp]
+theorem castSucc_predAbove_castSucc {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
+    a.castSucc.predAbove b.castSucc = (a.predAbove b).castSucc := by
+  obtain h | h := (lt_or_le (castSucc a) b)
+  · rw [Fin.predAbove_above _ _ h, Fin.predAbove_above _ _ (castSucc_lt_castSucc_iff.mpr h),
+    castSucc_pred_eq_pred_castSucc]
+  · rw [Fin.predAbove_below _ _ h, castSucc_castPred,
+    Fin.predAbove_below _ _ (castSucc_le_castSucc_iff.mpr h), castPred_castSucc]
+
+/-- `rev` commutes with `predAbove`. -/
+theorem rev_predAbove {n : ℕ} (p : Fin n) (i : Fin (n + 1)) :
+    (predAbove p i).rev = predAbove p.rev i.rev := by
+  rcases lt_or_le (castSucc p) i with (h | h)
+  · rw [predAbove_above _ _ h, rev_pred,
+    predAbove_below _ _ (by rwa [← rev_succ, rev_le_rev, ← castSucc_lt_iff_succ_le])]
+  · rw [predAbove_below _ _ h, rev_castPred,
+    predAbove_above _ _ (by rwa [← rev_succ, rev_lt_rev, ← le_castSucc_iff])]
+
 end PredAbove
 
 #align fin.coe_clamp Fin.coe_clamp

Prove repeat_comp_rev.

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -106,14 +106,10 @@ theorem val_injective : Function.Injective (@Fin.val n) :=
 #align fin.val_injective Fin.val_injective
 
 /-- If you actually have an element of `Fin n`, then the `n` is always positive -/
-lemma size_positive : Fin n → 0 < n
-  | ⟨x, h⟩ =>
-    match Nat.eq_or_lt_of_le (Nat.zero_le x) with
-    | Or.inl h_eq => h_eq ▸ h
-    | Or.inr h_lt => Nat.lt_trans h_lt h
+lemma size_positive : Fin n → 0 < n := Fin.pos
 
 lemma size_positive' [Nonempty (Fin n)] : 0 < n :=
-  ‹Nonempty (Fin n)›.elim fun i ↦ Fin.size_positive i
+  ‹Nonempty (Fin n)›.elim Fin.pos
 
 protected theorem prop (a : Fin n) : a.val < n :=
   a.2
@@ -1295,6 +1291,19 @@ theorem coe_modNat (i : Fin (m * n)) : (i.modNat : ℕ) = i % n :=
   rfl
 #align fin.coe_mod_nat Fin.coe_modNat
 
+theorem modNat_rev (i : Fin (m * n)) : i.rev.modNat = i.modNat.rev := by
+  ext
+  have H₁ : i % n + 1 ≤ n := i.modNat.is_lt
+  have H₂ : i / n < m := i.divNat.is_lt
+  simp only [coe_modNat, val_rev]
+  calc
+    (m * n - (i + 1)) % n = (m * n - ((i / n) * n + i % n + 1)) % n := by rw [Nat.div_add_mod']
+    _ = ((m - i / n - 1) * n + (n - (i % n + 1))) % n := by
+      rw [tsub_mul, one_mul, tsub_add_tsub_cancel _ H₁, tsub_mul, tsub_tsub, add_assoc]
+      exact le_mul_of_one_le_left' <| le_tsub_of_add_le_left H₂
+    _ = n - (i % n + 1) := by
+      rw [mul_comm, Nat.mul_add_mod, Nat.mod_eq_of_lt]; exact i.modNat.rev.is_lt
+
 end DivMod
 
 section Rec

predAbove and castPred are no longer directly related. This patch makes it so that they are, removing castLT from the definition of predAbove and thus making it more directly analogous to succAbove.

@@ -958,6 +958,10 @@ theorem castSucc_lt_succ_iff : castSucc a < succ b ↔ a ≤ b :=
 theorem le_of_castSucc_lt_of_succ_lt {a b : Fin (n + 1)} {i : Fin n}
     (hl : castSucc i < a) (hu : b < succ i) : b < a := (castSucc_lt_iff_succ_le.mp hl).trans_lt' hu
 
+theorem castSucc_lt_or_lt_succ (p : Fin (n + 1)) (i : Fin n) : castSucc i < p ∨ p < i.succ :=
+  (lt_or_le (castSucc i) p).imp id (fun h => le_castSucc_iff.mp h)
+#align fin.succ_above_lt_gt Fin.castSucc_lt_or_lt_succ
+
 theorem castSucc_injective (n : ℕ) : Injective (@Fin.castSucc n) :=
   (castSuccEmb : Fin n ↪o _).injective
 #align fin.cast_succ_injective Fin.castSucc_injective
@@ -1621,11 +1625,7 @@ theorem succAbove_lt_ge (p : Fin (n + 1)) (i : Fin n) : castSucc i < p ∨ p ≤
   lt_or_ge (castSucc i) p
 #align fin.succ_above_lt_ge Fin.succAbove_lt_ge
 
-/-- Embedding `i : Fin n` into `Fin (n + 1)` is always about some hole `p`. -/
-theorem succAbove_lt_gt (p : Fin (n + 1)) (i : Fin n) : castSucc i < p ∨ p < i.succ :=
-  Or.casesOn (succAbove_lt_ge p i) (fun h => Or.inl h) fun h =>
-    Or.inr (lt_of_le_of_lt h (castSucc_lt_succ i))
-#align fin.succ_above_lt_gt Fin.succAbove_lt_gt
+@[deprecated castSucc_lt_or_lt_succ] alias succAbove_lt_gt := castSucc_lt_or_lt_succ
 
 /-- Embedding `i : Fin n` into `Fin (n + 1)` using a pivot `p` that is greater
 results in a value that is less than `p`. -/
@@ -1812,8 +1812,8 @@ section PredAbove
 
 /-- `predAbove p i` embeds `i : Fin (n+1)` into `Fin n` by subtracting one if `p < i`. -/
 def predAbove (p : Fin n) (i : Fin (n + 1)) : Fin n :=
-  if h : castSucc p < i then i.pred ((ne_iff_vne i 0).mpr (Nat.not_eq_zero_of_lt h))
-  else i.castLT (Nat.lt_of_le_of_lt (Nat.ge_of_not_lt h) p.2)
+  if h : castSucc p < i then pred i ((zero_le _).trans_lt h).ne'
+  else castPred i ((le_of_not_lt h).trans_lt (castSucc_lt_last _)).ne
 #align fin.pred_above Fin.predAbove
 
 theorem predAbove_right_monotone (p : Fin n) : Monotone p.predAbove := fun a b H => by
@@ -1847,14 +1847,14 @@ theorem predAbove_zero {i : Fin (n + 2)} (hi : i ≠ 0) : predAbove 0 i = i.pred
   exact pos_iff_ne_zero.mpr hi
 #align fin.pred_above_zero Fin.predAbove_zero
 
-theorem predAbove_below (p : Fin n) (i : Fin (n + 1)) (h : i ≤ castSucc p) :
-    p.predAbove i = i.castLT (h.trans_lt (castSucc_lt_last _)) := by
-  simp [predAbove, h.not_lt]
+theorem predAbove_below (p : Fin n) (i : Fin (n + 1)) (h : i ≤ castSucc p)
+    (hi := (h.trans_lt (castSucc_lt_last _)).ne) :
+    p.predAbove i = i.castPred hi := dif_neg h.not_lt
 #align fin.pred_above_below Fin.predAbove_below
 
-theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : castSucc p < i) :
-    p.predAbove i = i.pred ((zero_le <| castSucc p).trans_lt h).ne.symm := by
-  simp [predAbove, h]
+theorem predAbove_above (p : Fin n) (i : Fin (n + 1)) (h : castSucc p < i)
+    (hi := ((zero_le _).trans_lt h).ne') :
+    p.predAbove i = i.pred hi := dif_pos h
 #align fin.pred_above_above Fin.predAbove_above
 
 @[simp]
@@ -1863,7 +1863,7 @@ theorem predAbove_right_last : predAbove (i : Fin (n + 1)) (Fin.last (n + 1)) =
 @[simp]
 theorem predAbove_last_castSucc {i : Fin (n + 1)} :
     predAbove (Fin.last n) (i.castSucc) = i := by
-  rw [predAbove_below _ _ ((castSucc_le_castSucc_iff).mpr (le_last _)), castLT_castSucc]
+  rw [predAbove_below _ _ ((castSucc_le_castSucc_iff).mpr (le_last _)), castPred_castSucc]
 @[simp]
 theorem predAbove_last_of_ne_last {i : Fin (n + 2)} (hi : i ≠ last (n + 1)):
     predAbove (Fin.last n) i = castPred i hi := by
@@ -1923,7 +1923,6 @@ theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (
     (hk := succAbove_ne_zero ha hb) :
     (a.pred ha).succAbove (b.pred hb) = (a.succAbove b).pred hk := by
   obtain hbelow | habove := lt_or_le (castSucc b) a
-  -- `rwa` uses them
   · rw [Fin.succAbove_below]
     · rwa [castSucc_pred_eq_pred_castSucc, Fin.pred_inj, Fin.succAbove_below]
     · rwa [castSucc_pred_eq_pred_castSucc, pred_lt_pred_iff]
@@ -1937,20 +1936,11 @@ theorem pred_succAbove_pred {a : Fin (n + 2)} {b : Fin (n + 1)} (ha : a ≠ 0) (
 @[simp]
 theorem succ_predAbove_succ {n : ℕ} (a : Fin n) (b : Fin (n + 1)) :
     a.succ.predAbove b.succ = (a.predAbove b).succ := by
-  obtain h₁ | h₂ := lt_or_le (castSucc a) b
-  · rw [Fin.predAbove_above _ _ h₁, Fin.succ_pred, Fin.predAbove_above, Fin.pred_succ]
-    simpa only [lt_iff_val_lt_val, coe_castSucc, val_succ, add_lt_add_iff_right] using
-      h₁
-  · cases' n with n
-    · exfalso
-      exact not_lt_zero' a.is_lt
-    · rw [Fin.predAbove_below a b h₂,
-        Fin.predAbove_below a.succ b.succ
-          (by
-            simpa only [le_iff_val_le_val, val_succ, coe_castSucc, add_le_add_iff_right]
-              using h₂)]
-      ext
-      simp only [val_last, coe_castLT, val_succ]
+  obtain h | h := (lt_or_le (castSucc a) b)
+  · rw [Fin.predAbove_above _ _ h, succ_pred, Fin.predAbove_above, pred_succ]
+    rwa [castSucc_lt_succ_iff, ← castSucc_lt_iff_succ_le]
+  · rw [Fin.predAbove_below _ _ h, Fin.predAbove_below, succ_castPred_eq_castPred_succ]
+    rwa [succ_le_castSucc_iff, ← le_castSucc_iff]
 #align fin.succ_pred_above_succ Fin.succ_predAbove_succ
 
 end PredAbove