topology.metric_space.contracting ⟷ Mathlib.Topology.MetricSpace.Contracting

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

@@ -441,7 +441,7 @@ theorem isFixedPt_fixedPoint_iterate {n : ℕ} (hf : ContractingWith K (f^[n]))
   set x := hf.fixed_point (f^[n])
   have hx : (f^[n]) x = x := hf.fixed_point_is_fixed_pt
   have := hf.to_lipschitz_with.dist_le_mul x (f x)
-  rw [← iterate_succ_apply, iterate_succ_apply', hx] at this 
+  rw [← iterate_succ_apply, iterate_succ_apply', hx] at this
   contrapose! this
   have := dist_pos.2 (Ne.symm this)
   simpa only [NNReal.coe_one, one_mul, NNReal.val_eq_coe] using (mul_lt_mul_right this).mpr hf.left

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

@@ -98,7 +98,7 @@ theorem edist_le_of_fixedPoint (hf : ContractingWith K f) {x y} (h : edist x y 
 theorem eq_or_edist_eq_top_of_fixedPoints (hf : ContractingWith K f) {x y} (hx : IsFixedPt f x)
     (hy : IsFixedPt f y) : x = y ∨ edist x y = ∞ :=
   by
-  refine' or_iff_not_imp_right.2 fun h => edist_le_zero.1 _
+  refine' Classical.or_iff_not_imp_right.2 fun h => edist_le_zero.1 _
   simpa only [hx.eq, edist_self, add_zero, ENNReal.zero_div] using hf.edist_le_of_fixed_point h hy
 #align contracting_with.eq_or_edist_eq_top_of_fixed_points ContractingWith.eq_or_edist_eq_top_of_fixedPoints
 -/

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

@@ -3,9 +3,9 @@ Copyright (c) 2019 Rohan Mitta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
 -/
-import Mathbin.Analysis.SpecificLimits.Basic
-import Mathbin.Data.Setoid.Basic
-import Mathbin.Dynamics.FixedPoints.Topology
+import Analysis.SpecificLimits.Basic
+import Data.Setoid.Basic
+import Dynamics.FixedPoints.Topology
 
 #align_import topology.metric_space.contracting from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Rohan Mitta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.metric_space.contracting
-! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecificLimits.Basic
 import Mathbin.Data.Setoid.Basic
 import Mathbin.Dynamics.FixedPoints.Topology
 
+#align_import topology.metric_space.contracting from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
+
 /-!
 # Contracting maps
 

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

@@ -61,16 +61,23 @@ theorem toLipschitzWith (hf : ContractingWith K f) : LipschitzWith K f :=
 #align contracting_with.to_lipschitz_with ContractingWith.toLipschitzWith
 -/
 
+#print ContractingWith.one_sub_K_pos' /-
 theorem one_sub_K_pos' (hf : ContractingWith K f) : (0 : ℝ≥0∞) < 1 - K := by simp [hf.1]
 #align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'
+-/
 
+#print ContractingWith.one_sub_K_ne_zero /-
 theorem one_sub_K_ne_zero (hf : ContractingWith K f) : (1 : ℝ≥0∞) - K ≠ 0 :=
   ne_of_gt hf.one_sub_K_pos'
 #align contracting_with.one_sub_K_ne_zero ContractingWith.one_sub_K_ne_zero
+-/
 
+#print ContractingWith.one_sub_K_ne_top /-
 theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ := by norm_cast; exact ENNReal.coe_ne_top
 #align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_top
+-/
 
+#print ContractingWith.edist_inequality /-
 theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞) :
     edist x y ≤ (edist x (f x) + edist y (f y)) / (1 - K) :=
   suffices edist x y ≤ edist x (f x) + edist y (f y) + K * edist x y by
@@ -81,18 +88,23 @@ theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞
     _ = edist x (f x) + edist y (f y) + edist (f x) (f y) := by rw [edist_comm y, add_right_comm]
     _ ≤ edist x (f x) + edist y (f y) + K * edist x y := add_le_add le_rfl (hf.2 _ _)
 #align contracting_with.edist_inequality ContractingWith.edist_inequality
+-/
 
+#print ContractingWith.edist_le_of_fixedPoint /-
 theorem edist_le_of_fixedPoint (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞)
     (hy : IsFixedPt f y) : edist x y ≤ edist x (f x) / (1 - K) := by
   simpa only [hy.eq, edist_self, add_zero] using hf.edist_inequality h
 #align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixedPoint
+-/
 
+#print ContractingWith.eq_or_edist_eq_top_of_fixedPoints /-
 theorem eq_or_edist_eq_top_of_fixedPoints (hf : ContractingWith K f) {x y} (hx : IsFixedPt f x)
     (hy : IsFixedPt f y) : x = y ∨ edist x y = ∞ :=
   by
   refine' or_iff_not_imp_right.2 fun h => edist_le_zero.1 _
   simpa only [hx.eq, edist_self, add_zero, ENNReal.zero_div] using hf.edist_le_of_fixed_point h hy
 #align contracting_with.eq_or_edist_eq_top_of_fixed_points ContractingWith.eq_or_edist_eq_top_of_fixedPoints
+-/
 
 #print ContractingWith.restrict /-
 /-- If a map `f` is `contracting_with K`, and `s` is a forward-invariant set, then
@@ -103,8 +115,7 @@ theorem restrict (hf : ContractingWith K f) {s : Set α} (hs : MapsTo f s s) :
 #align contracting_with.restrict ContractingWith.restrict
 -/
 
-include cs
-
+#print ContractingWith.exists_fixedPoint /-
 /-- Banach fixed-point theorem, contraction mapping theorem, `emetric_space` version.
 A contracting map on a complete metric space has a fixed point.
 We include more conclusions in this theorem to avoid proving them again later.
@@ -124,9 +135,11 @@ theorem exists_fixedPoint (hf : ContractingWith K f) (x : α) (hx : edist x (f x
     edist_le_of_edist_le_geometric_of_tendsto K (edist x (f x))
       (hf.toLipschitzWith.edist_iterate_succ_le_geometric x) hy⟩
 #align contracting_with.exists_fixed_point ContractingWith.exists_fixedPoint
+-/
 
 variable (f)
 
+#print ContractingWith.efixedPoint /-
 -- avoid `efixed_point _` in pretty printer
 /-- Let `x` be a point of a complete emetric space. Suppose that `f` is a contracting map,
 and `edist x (f x) ≠ ∞`. Then `efixed_point` is the unique fixed point of `f`
@@ -134,36 +147,48 @@ in `emetric.ball x ∞`. -/
 noncomputable def efixedPoint (hf : ContractingWith K f) (x : α) (hx : edist x (f x) ≠ ∞) : α :=
   Classical.choose <| hf.exists_fixedPoint x hx
 #align contracting_with.efixed_point ContractingWith.efixedPoint
+-/
 
 variable {f}
 
+#print ContractingWith.efixedPoint_isFixedPt /-
 theorem efixedPoint_isFixedPt (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint f hf x hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).1
 #align contracting_with.efixed_point_is_fixed_pt ContractingWith.efixedPoint_isFixedPt
+-/
 
+#print ContractingWith.tendsto_iterate_efixedPoint /-
 theorem tendsto_iterate_efixedPoint (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     Tendsto (fun n => (f^[n]) x) atTop (𝓝 <| efixedPoint f hf x hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.1
 #align contracting_with.tendsto_iterate_efixed_point ContractingWith.tendsto_iterate_efixedPoint
+-/
 
+#print ContractingWith.apriori_edist_iterate_efixedPoint_le /-
 theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
     (hx : edist x (f x) ≠ ∞) (n : ℕ) :
     edist ((f^[n]) x) (efixedPoint f hf x hx) ≤ edist x (f x) * K ^ n / (1 - K) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.2 n
 #align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_le
+-/
 
+#print ContractingWith.edist_efixedPoint_le /-
 theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) ≤ edist x (f x) / (1 - K) := by
   convert hf.apriori_edist_iterate_efixed_point_le hx 0; simp only [pow_zero, mul_one]
 #align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_le
+-/
 
+#print ContractingWith.edist_efixedPoint_lt_top /-
 theorem edist_efixedPoint_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) < ∞ :=
   (hf.edist_efixedPoint_le hx).trans_lt
     (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
 #align contracting_with.edist_efixed_point_lt_top ContractingWith.edist_efixedPoint_lt_top
+-/
 
+#print ContractingWith.efixedPoint_eq_of_edist_lt_top /-
 theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞)
     {y : α} (hy : edist y (f y) ≠ ∞) (h : edist x y ≠ ∞) :
     efixedPoint f hf x hx = efixedPoint f hf y hy :=
@@ -176,9 +201,9 @@ theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx :
   trans y
   exacts [lt_top_iff_ne_top.2 h, hf.edist_efixed_point_lt_top hy]
 #align contracting_with.efixed_point_eq_of_edist_lt_top ContractingWith.efixedPoint_eq_of_edist_lt_top
+-/
 
-omit cs
-
+#print ContractingWith.exists_fixedPoint' /-
 /-- Banach fixed-point theorem for maps contracting on a complete subset. -/
 theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
@@ -195,9 +220,11 @@ theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s
   · convert hle n
     rw [maps_to.iterate_restrict, eq_comm, maps_to.coe_restrict_apply, Subtype.coe_mk]
 #align contracting_with.exists_fixed_point' ContractingWith.exists_fixedPoint'
+-/
 
 variable (f)
 
+#print ContractingWith.efixedPoint' /-
 -- avoid `efixed_point _` in pretty printer
 /-- Let `s` be a complete forward-invariant set of a self-map `f`. If `f` contracts on `s`
 and `x ∈ s` satisfies `edist x (f x) ≠ ∞`, then `efixed_point'` is the unique fixed point
@@ -207,34 +234,44 @@ noncomputable def efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f
     α :=
   Classical.choose <| hf.exists_fixedPoint' hsc hsf hxs hx
 #align contracting_with.efixed_point' ContractingWith.efixedPoint'
+-/
 
 variable {f}
 
+#print ContractingWith.efixedPoint_mem' /-
 theorem efixedPoint_mem' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     efixedPoint' f hsc hsf hf x hxs hx ∈ s :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).fst
 #align contracting_with.efixed_point_mem' ContractingWith.efixedPoint_mem'
+-/
 
+#print ContractingWith.efixedPoint_isFixedPt' /-
 theorem efixedPoint_isFixedPt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint' f hsc hsf hf x hxs hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.1
 #align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_isFixedPt'
+-/
 
+#print ContractingWith.tendsto_iterate_efixedPoint' /-
 theorem tendsto_iterate_efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     Tendsto (fun n => (f^[n]) x) atTop (𝓝 <| efixedPoint' f hsc hsf hf x hxs hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.2.1
 #align contracting_with.tendsto_iterate_efixed_point' ContractingWith.tendsto_iterate_efixedPoint'
+-/
 
+#print ContractingWith.apriori_edist_iterate_efixedPoint_le' /-
 theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞)
     (n : ℕ) :
     edist ((f^[n]) x) (efixedPoint' f hsc hsf hf x hxs hx) ≤ edist x (f x) * K ^ n / (1 - K) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.2.2 n
 #align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'
+-/
 
+#print ContractingWith.edist_efixedPoint_le' /-
 theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) ≤ edist x (f x) / (1 - K) :=
@@ -242,14 +279,18 @@ theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f
   convert hf.apriori_edist_iterate_efixed_point_le' hsc hsf hxs hx 0
   rw [pow_zero, mul_one]
 #align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixedPoint_le'
+-/
 
+#print ContractingWith.edist_efixedPoint_lt_top' /-
 theorem edist_efixedPoint_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) < ∞ :=
   (hf.edist_efixedPoint_le' hsc hsf hxs hx).trans_lt
     (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
 #align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixedPoint_lt_top'
+-/
 
+#print ContractingWith.efixedPoint_eq_of_edist_lt_top' /-
 /-- If a globally contracting map `f` has two complete forward-invariant sets `s`, `t`,
 and `x ∈ s` is at a finite distance from `y ∈ t`, then the `efixed_point'` constructed by `x`
 is the same as the `efixed_point'` constructed by `y`.
@@ -272,6 +313,7 @@ theorem efixedPoint_eq_of_edist_lt_top' (hf : ContractingWith K f) {s : Set α}
   exact lt_top_iff_ne_top.2 hxy
   apply edist_efixed_point_lt_top'
 #align contracting_with.efixed_point_eq_of_edist_lt_top' ContractingWith.efixedPoint_eq_of_edist_lt_top'
+-/
 
 end ContractingWith
 
@@ -279,16 +321,19 @@ namespace ContractingWith
 
 variable [MetricSpace α] {K : ℝ≥0} {f : α → α} (hf : ContractingWith K f)
 
-include hf
-
+#print ContractingWith.one_sub_K_pos /-
 theorem one_sub_K_pos (hf : ContractingWith K f) : (0 : ℝ) < 1 - K :=
   sub_pos.2 hf.1
 #align contracting_with.one_sub_K_pos ContractingWith.one_sub_K_pos
+-/
 
+#print ContractingWith.dist_le_mul /-
 theorem dist_le_mul (x y : α) : dist (f x) (f y) ≤ K * dist x y :=
   hf.toLipschitzWith.dist_le_mul x y
 #align contracting_with.dist_le_mul ContractingWith.dist_le_mul
+-/
 
+#print ContractingWith.dist_inequality /-
 theorem dist_inequality (x y) : dist x y ≤ (dist x (f x) + dist y (f y)) / (1 - K) :=
   suffices dist x y ≤ dist x (f x) + dist y (f y) + K * dist x y by
     rwa [le_div_iff hf.one_sub_K_pos, mul_comm, sub_mul, one_mul, sub_le_iff_le_add]
@@ -296,10 +341,13 @@ theorem dist_inequality (x y) : dist x y ≤ (dist x (f x) + dist y (f y)) / (1
     dist x y ≤ dist x (f x) + dist y (f y) + dist (f x) (f y) := dist_triangle4_right _ _ _ _
     _ ≤ dist x (f x) + dist y (f y) + K * dist x y := add_le_add_left (hf.dist_le_mul _ _) _
 #align contracting_with.dist_inequality ContractingWith.dist_inequality
+-/
 
+#print ContractingWith.dist_le_of_fixedPoint /-
 theorem dist_le_of_fixedPoint (x) {y} (hy : IsFixedPt f y) : dist x y ≤ dist x (f x) / (1 - K) := by
   simpa only [hy.eq, dist_self, add_zero] using hf.dist_inequality x y
 #align contracting_with.dist_le_of_fixed_point ContractingWith.dist_le_of_fixedPoint
+-/
 
 #print ContractingWith.fixedPoint_unique' /-
 theorem fixedPoint_unique' {x y} (hx : IsFixedPt f x) (hy : IsFixedPt f y) : x = y :=
@@ -307,6 +355,7 @@ theorem fixedPoint_unique' {x y} (hx : IsFixedPt f x) (hy : IsFixedPt f y) : x =
 #align contracting_with.fixed_point_unique' ContractingWith.fixedPoint_unique'
 -/
 
+#print ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le' /-
 /-- Let `f` be a contracting map with constant `K`; let `g` be another map uniformly
 `C`-close to `f`. If `x` and `y` are their fixed points, then `dist x y ≤ C / (1 - K)`. -/
 theorem dist_fixedPoint_fixedPoint_of_dist_le' (g : α → α) {x y} (hx : IsFixedPt f x)
@@ -317,6 +366,7 @@ theorem dist_fixedPoint_fixedPoint_of_dist_le' (g : α → α) {x y} (hx : IsFix
     _ = dist (f y) (g y) / (1 - K) := by rw [hy.eq, dist_comm]
     _ ≤ C / (1 - K) := (div_le_div_right hf.one_sub_K_pos).2 (hfg y)
 #align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le'
+-/
 
 noncomputable section
 
@@ -346,21 +396,27 @@ theorem fixedPoint_unique {x} (hx : IsFixedPt f x) : x = fixedPoint f hf :=
 #align contracting_with.fixed_point_unique ContractingWith.fixedPoint_unique
 -/
 
+#print ContractingWith.dist_fixedPoint_le /-
 theorem dist_fixedPoint_le (x) : dist x (fixedPoint f hf) ≤ dist x (f x) / (1 - K) :=
   hf.dist_le_of_fixedPoint x hf.fixedPoint_isFixedPt
 #align contracting_with.dist_fixed_point_le ContractingWith.dist_fixedPoint_le
+-/
 
+#print ContractingWith.aposteriori_dist_iterate_fixedPoint_le /-
 /-- Aposteriori estimates on the convergence of iterates to the fixed point. -/
 theorem aposteriori_dist_iterate_fixedPoint_le (x n) :
     dist ((f^[n]) x) (fixedPoint f hf) ≤ dist ((f^[n]) x) ((f^[n + 1]) x) / (1 - K) := by
   rw [iterate_succ']; apply hf.dist_fixed_point_le
 #align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_le
+-/
 
+#print ContractingWith.apriori_dist_iterate_fixedPoint_le /-
 theorem apriori_dist_iterate_fixedPoint_le (x n) :
     dist ((f^[n]) x) (fixedPoint f hf) ≤ dist x (f x) * K ^ n / (1 - K) :=
   le_trans (hf.aposteriori_dist_iterate_fixedPoint_le x n) <|
     (div_le_div_right hf.one_sub_K_pos).2 <| hf.toLipschitzWith.dist_iterate_succ_le_geometric x n
 #align contracting_with.apriori_dist_iterate_fixed_point_le ContractingWith.apriori_dist_iterate_fixedPoint_le
+-/
 
 #print ContractingWith.tendsto_iterate_fixedPoint /-
 theorem tendsto_iterate_fixedPoint (x) :
@@ -372,12 +428,12 @@ theorem tendsto_iterate_fixedPoint (x) :
 #align contracting_with.tendsto_iterate_fixed_point ContractingWith.tendsto_iterate_fixedPoint
 -/
 
+#print ContractingWith.fixedPoint_lipschitz_in_map /-
 theorem fixedPoint_lipschitz_in_map {g : α → α} (hg : ContractingWith K g) {C}
     (hfg : ∀ z, dist (f z) (g z) ≤ C) : dist (fixedPoint f hf) (fixedPoint g hg) ≤ C / (1 - K) :=
   hf.dist_fixedPoint_fixedPoint_of_dist_le' g hf.fixedPoint_isFixedPt hg.fixedPoint_isFixedPt hfg
 #align contracting_with.fixed_point_lipschitz_in_map ContractingWith.fixedPoint_lipschitz_in_map
-
-omit hf
+-/
 
 #print ContractingWith.isFixedPt_fixedPoint_iterate /-
 /-- If a map `f` has a contracting iterate `f^[n]`, then the fixed point of `f^[n]` is also a fixed

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

@@ -80,7 +80,6 @@ theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞
     edist x y ≤ edist x (f x) + edist (f x) (f y) + edist (f y) y := edist_triangle4 _ _ _ _
     _ = edist x (f x) + edist y (f y) + edist (f x) (f y) := by rw [edist_comm y, add_right_comm]
     _ ≤ edist x (f x) + edist y (f y) + K * edist x y := add_le_add le_rfl (hf.2 _ _)
-    
 #align contracting_with.edist_inequality ContractingWith.edist_inequality
 
 theorem edist_le_of_fixedPoint (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞)
@@ -296,7 +295,6 @@ theorem dist_inequality (x y) : dist x y ≤ (dist x (f x) + dist y (f y)) / (1
   calc
     dist x y ≤ dist x (f x) + dist y (f y) + dist (f x) (f y) := dist_triangle4_right _ _ _ _
     _ ≤ dist x (f x) + dist y (f y) + K * dist x y := add_le_add_left (hf.dist_le_mul _ _) _
-    
 #align contracting_with.dist_inequality ContractingWith.dist_inequality
 
 theorem dist_le_of_fixedPoint (x) {y} (hy : IsFixedPt f y) : dist x y ≤ dist x (f x) / (1 - K) := by
@@ -318,7 +316,6 @@ theorem dist_fixedPoint_fixedPoint_of_dist_le' (g : α → α) {x y} (hx : IsFix
     _ ≤ dist y (f y) / (1 - K) := (hf.dist_le_of_fixedPoint y hx)
     _ = dist (f y) (g y) / (1 - K) := by rw [hy.eq, dist_comm]
     _ ≤ C / (1 - K) := (div_le_div_right hf.one_sub_K_pos).2 (hfg y)
-    
 #align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le'
 
 noncomputable section

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

@@ -191,7 +191,7 @@ theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s
   haveI := hsc.complete_space_coe
   rcases hf.exists_fixed_point ⟨x, hxs⟩ hx with ⟨y, hfy, h_tendsto, hle⟩
   refine' ⟨y, y.2, Subtype.ext_iff_val.1 hfy, _, fun n => _⟩
-  · convert(continuous_subtype_coe.tendsto _).comp h_tendsto; ext n
+  · convert (continuous_subtype_coe.tendsto _).comp h_tendsto; ext n
     simp only [(· ∘ ·), maps_to.iterate_restrict, maps_to.coe_restrict_apply, Subtype.coe_mk]
   · convert hle n
     rw [maps_to.iterate_restrict, eq_comm, maps_to.coe_restrict_apply, Subtype.coe_mk]

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

@@ -175,7 +175,7 @@ theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx :
   change edist_lt_top_setoid.rel _ _
   trans x; · symm; exact hf.edist_efixed_point_lt_top hx
   trans y
-  exacts[lt_top_iff_ne_top.2 h, hf.edist_efixed_point_lt_top hy]
+  exacts [lt_top_iff_ne_top.2 h, hf.edist_efixed_point_lt_top hy]
 #align contracting_with.efixed_point_eq_of_edist_lt_top ContractingWith.efixedPoint_eq_of_edist_lt_top
 
 omit cs
@@ -391,7 +391,7 @@ theorem isFixedPt_fixedPoint_iterate {n : ℕ} (hf : ContractingWith K (f^[n]))
   set x := hf.fixed_point (f^[n])
   have hx : (f^[n]) x = x := hf.fixed_point_is_fixed_pt
   have := hf.to_lipschitz_with.dist_le_mul x (f x)
-  rw [← iterate_succ_apply, iterate_succ_apply', hx] at this
+  rw [← iterate_succ_apply, iterate_succ_apply', hx] at this 
   contrapose! this
   have := dist_pos.2 (Ne.symm this)
   simpa only [NNReal.coe_one, one_mul, NNReal.val_eq_coe] using (mul_lt_mul_right this).mpr hf.left

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

@@ -36,7 +36,7 @@ contracting map, fixed point, Banach fixed point theorem
 -/
 
 
-open NNReal Topology Classical ENNReal
+open scoped NNReal Topology Classical ENNReal
 
 open Filter Function
 

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

@@ -61,40 +61,16 @@ theorem toLipschitzWith (hf : ContractingWith K f) : LipschitzWith K f :=
 #align contracting_with.to_lipschitz_with ContractingWith.toLipschitzWith
 -/
 
-/- warning: contracting_with.one_sub_K_pos' -> ContractingWith.one_sub_K_pos' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
-Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'ₓ'. -/
 theorem one_sub_K_pos' (hf : ContractingWith K f) : (0 : ℝ≥0∞) < 1 - K := by simp [hf.1]
 #align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'
 
-/- warning: contracting_with.one_sub_K_ne_zero -> ContractingWith.one_sub_K_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
-Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_ne_zero ContractingWith.one_sub_K_ne_zeroₓ'. -/
 theorem one_sub_K_ne_zero (hf : ContractingWith K f) : (1 : ℝ≥0∞) - K ≠ 0 :=
   ne_of_gt hf.one_sub_K_pos'
 #align contracting_with.one_sub_K_ne_zero ContractingWith.one_sub_K_ne_zero
 
-/- warning: contracting_with.one_sub_K_ne_top -> ContractingWith.one_sub_K_ne_top is a dubious translation:
-lean 3 declaration is
-  forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
-but is expected to have type
-  forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
-Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_topₓ'. -/
 theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ := by norm_cast; exact ENNReal.coe_ne_top
 #align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_top
 
-/- warning: contracting_with.edist_inequality -> ContractingWith.edist_inequality is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
-Case conversion may be inaccurate. Consider using '#align contracting_with.edist_inequality ContractingWith.edist_inequalityₓ'. -/
 theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞) :
     edist x y ≤ (edist x (f x) + edist y (f y)) / (1 - K) :=
   suffices edist x y ≤ edist x (f x) + edist y (f y) + K * edist x y by
@@ -107,23 +83,11 @@ theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞
     
 #align contracting_with.edist_inequality ContractingWith.edist_inequality
 
-/- warning: contracting_with.edist_le_of_fixed_point -> ContractingWith.edist_le_of_fixedPoint is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
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-Case conversion may be inaccurate. Consider using '#align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixedPointₓ'. -/
 theorem edist_le_of_fixedPoint (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞)
     (hy : IsFixedPt f y) : edist x y ≤ edist x (f x) / (1 - K) := by
   simpa only [hy.eq, edist_self, add_zero] using hf.edist_inequality h
 #align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixedPoint
 
-/- warning: contracting_with.eq_or_edist_eq_top_of_fixed_points -> ContractingWith.eq_or_edist_eq_top_of_fixedPoints is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Function.IsFixedPt.{u1} α f x) -> (Function.IsFixedPt.{u1} α f y) -> (Or (Eq.{succ u1} α x y) (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Function.IsFixedPt.{u1} α f x) -> (Function.IsFixedPt.{u1} α f y) -> (Or (Eq.{succ u1} α x y) (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))))
-Case conversion may be inaccurate. Consider using '#align contracting_with.eq_or_edist_eq_top_of_fixed_points ContractingWith.eq_or_edist_eq_top_of_fixedPointsₓ'. -/
 theorem eq_or_edist_eq_top_of_fixedPoints (hf : ContractingWith K f) {x y} (hx : IsFixedPt f x)
     (hy : IsFixedPt f y) : x = y ∨ edist x y = ∞ :=
   by
@@ -142,12 +106,6 @@ theorem restrict (hf : ContractingWith K f) {s : Set α} (hs : MapsTo f s s) :
 
 include cs
 
-/- warning: contracting_with.exists_fixed_point -> ContractingWith.exists_fixedPoint is a dubious translation:
-lean 3 declaration is
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-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))
-Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point ContractingWith.exists_fixedPointₓ'. -/
 /-- Banach fixed-point theorem, contraction mapping theorem, `emetric_space` version.
 A contracting map on a complete metric space has a fixed point.
 We include more conclusions in this theorem to avoid proving them again later.
@@ -170,12 +128,6 @@ theorem exists_fixedPoint (hf : ContractingWith K f) (x : α) (hx : edist x (f x
 
 variable (f)
 
-/- warning: contracting_with.efixed_point -> ContractingWith.efixedPoint is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point ContractingWith.efixedPointₓ'. -/
 -- avoid `efixed_point _` in pretty printer
 /-- Let `x` be a point of a complete emetric space. Suppose that `f` is a contracting map,
 and `edist x (f x) ≠ ∞`. Then `efixed_point` is the unique fixed point of `f`
@@ -186,69 +138,33 @@ noncomputable def efixedPoint (hf : ContractingWith K f) (x : α) (hx : edist x
 
 variable {f}
 
-/- warning: contracting_with.efixed_point_is_fixed_pt -> ContractingWith.efixedPoint_isFixedPt is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_is_fixed_pt ContractingWith.efixedPoint_isFixedPtₓ'. -/
 theorem efixedPoint_isFixedPt (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint f hf x hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).1
 #align contracting_with.efixed_point_is_fixed_pt ContractingWith.efixedPoint_isFixedPt
 
-/- warning: contracting_with.tendsto_iterate_efixed_point -> ContractingWith.tendsto_iterate_efixedPoint is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx))
-Case conversion may be inaccurate. Consider using '#align contracting_with.tendsto_iterate_efixed_point ContractingWith.tendsto_iterate_efixedPointₓ'. -/
 theorem tendsto_iterate_efixedPoint (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     Tendsto (fun n => (f^[n]) x) atTop (𝓝 <| efixedPoint f hf x hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.1
 #align contracting_with.tendsto_iterate_efixed_point ContractingWith.tendsto_iterate_efixedPoint
 
-/- warning: contracting_with.apriori_edist_iterate_efixed_point_le -> ContractingWith.apriori_edist_iterate_efixedPoint_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_leₓ'. -/
 theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
     (hx : edist x (f x) ≠ ∞) (n : ℕ) :
     edist ((f^[n]) x) (efixedPoint f hf x hx) ≤ edist x (f x) * K ^ n / (1 - K) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.2 n
 #align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_le
 
-/- warning: contracting_with.edist_efixed_point_le -> ContractingWith.edist_efixedPoint_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_leₓ'. -/
 theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) ≤ edist x (f x) / (1 - K) := by
   convert hf.apriori_edist_iterate_efixed_point_le hx 0; simp only [pow_zero, mul_one]
 #align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_le
 
-/- warning: contracting_with.edist_efixed_point_lt_top -> ContractingWith.edist_efixedPoint_lt_top is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
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-Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_lt_top ContractingWith.edist_efixedPoint_lt_topₓ'. -/
 theorem edist_efixedPoint_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) < ∞ :=
   (hf.edist_efixedPoint_le hx).trans_lt
     (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
 #align contracting_with.edist_efixed_point_lt_top ContractingWith.edist_efixedPoint_lt_top
 
-/- warning: contracting_with.efixed_point_eq_of_edist_lt_top -> ContractingWith.efixedPoint_eq_of_edist_lt_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) {y : α} (hy : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Eq.{succ u1} α (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf y hy))
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-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_eq_of_edist_lt_top ContractingWith.efixedPoint_eq_of_edist_lt_topₓ'. -/
 theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞)
     {y : α} (hy : edist y (f y) ≠ ∞) (h : edist x y ≠ ∞) :
     efixedPoint f hf x hx = efixedPoint f hf y hy :=
@@ -264,9 +180,6 @@ theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx :
 
 omit cs
 
-/- warning: contracting_with.exists_fixed_point' -> ContractingWith.exists_fixedPoint' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point' ContractingWith.exists_fixedPoint'ₓ'. -/
 /-- Banach fixed-point theorem for maps contracting on a complete subset. -/
 theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
@@ -286,12 +199,6 @@ theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s
 
 variable (f)
 
-/- warning: contracting_with.efixed_point' -> ContractingWith.efixedPoint' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point' ContractingWith.efixedPoint'ₓ'. -/
 -- avoid `efixed_point _` in pretty printer
 /-- Let `s` be a complete forward-invariant set of a self-map `f`. If `f` contracts on `s`
 and `x ∈ s` satisfies `edist x (f x) ≠ ∞`, then `efixed_point'` is the unique fixed point
@@ -304,48 +211,24 @@ noncomputable def efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f
 
 variable {f}
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_mem' ContractingWith.efixedPoint_mem'ₓ'. -/
 theorem efixedPoint_mem' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     efixedPoint' f hsc hsf hf x hxs hx ∈ s :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).fst
 #align contracting_with.efixed_point_mem' ContractingWith.efixedPoint_mem'
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_isFixedPt'ₓ'. -/
 theorem efixedPoint_isFixedPt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint' f hsc hsf hf x hxs hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.1
 #align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_isFixedPt'
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.tendsto_iterate_efixed_point' ContractingWith.tendsto_iterate_efixedPoint'ₓ'. -/
 theorem tendsto_iterate_efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     Tendsto (fun n => (f^[n]) x) atTop (𝓝 <| efixedPoint' f hsc hsf hf x hxs hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.2.1
 #align contracting_with.tendsto_iterate_efixed_point' ContractingWith.tendsto_iterate_efixedPoint'
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'ₓ'. -/
 theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞)
     (n : ℕ) :
@@ -353,12 +236,6 @@ theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s)
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.2.2 n
 #align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixedPoint_le'ₓ'. -/
 theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) ≤ edist x (f x) / (1 - K) :=
@@ -367,12 +244,6 @@ theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f
   rw [pow_zero, mul_one]
 #align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixedPoint_le'
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixedPoint_lt_top'ₓ'. -/
 theorem edist_efixedPoint_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) < ∞ :=
@@ -380,9 +251,6 @@ theorem edist_efixedPoint_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : MapsT
     (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
 #align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixedPoint_lt_top'
 
-/- warning: contracting_with.efixed_point_eq_of_edist_lt_top' -> ContractingWith.efixedPoint_eq_of_edist_lt_top' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_eq_of_edist_lt_top' ContractingWith.efixedPoint_eq_of_edist_lt_top'ₓ'. -/
 /-- If a globally contracting map `f` has two complete forward-invariant sets `s`, `t`,
 and `x ∈ s` is at a finite distance from `y ∈ t`, then the `efixed_point'` constructed by `x`
 is the same as the `efixed_point'` constructed by `y`.
@@ -414,32 +282,14 @@ variable [MetricSpace α] {K : ℝ≥0} {f : α → α} (hf : ContractingWith K
 
 include hf
 
-/- warning: contracting_with.one_sub_K_pos -> ContractingWith.one_sub_K_pos is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K)))
-Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_pos ContractingWith.one_sub_K_posₓ'. -/
 theorem one_sub_K_pos (hf : ContractingWith K f) : (0 : ℝ) < 1 - K :=
   sub_pos.2 hf.1
 #align contracting_with.one_sub_K_pos ContractingWith.one_sub_K_pos
 
-/- warning: contracting_with.dist_le_mul -> ContractingWith.dist_le_mul is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) (y : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align contracting_with.dist_le_mul ContractingWith.dist_le_mulₓ'. -/
 theorem dist_le_mul (x y : α) : dist (f x) (f y) ≤ K * dist x y :=
   hf.toLipschitzWith.dist_le_mul x y
 #align contracting_with.dist_le_mul ContractingWith.dist_le_mul
 
-/- warning: contracting_with.dist_inequality -> ContractingWith.dist_inequality is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) (y : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K))))
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-Case conversion may be inaccurate. Consider using '#align contracting_with.dist_inequality ContractingWith.dist_inequalityₓ'. -/
 theorem dist_inequality (x y) : dist x y ≤ (dist x (f x) + dist y (f y)) / (1 - K) :=
   suffices dist x y ≤ dist x (f x) + dist y (f y) + K * dist x y by
     rwa [le_div_iff hf.one_sub_K_pos, mul_comm, sub_mul, one_mul, sub_le_iff_le_add]
@@ -449,12 +299,6 @@ theorem dist_inequality (x y) : dist x y ≤ (dist x (f x) + dist y (f y)) / (1
     
 #align contracting_with.dist_inequality ContractingWith.dist_inequality
 
-/- warning: contracting_with.dist_le_of_fixed_point -> ContractingWith.dist_le_of_fixedPoint is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) {y : α}, (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))))
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-Case conversion may be inaccurate. Consider using '#align contracting_with.dist_le_of_fixed_point ContractingWith.dist_le_of_fixedPointₓ'. -/
 theorem dist_le_of_fixedPoint (x) {y} (hy : IsFixedPt f y) : dist x y ≤ dist x (f x) / (1 - K) := by
   simpa only [hy.eq, dist_self, add_zero] using hf.dist_inequality x y
 #align contracting_with.dist_le_of_fixed_point ContractingWith.dist_le_of_fixedPoint
@@ -465,12 +309,6 @@ theorem fixedPoint_unique' {x y} (hx : IsFixedPt f x) (hy : IsFixedPt f y) : x =
 #align contracting_with.fixed_point_unique' ContractingWith.fixedPoint_unique'
 -/
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le'ₓ'. -/
 /-- Let `f` be a contracting map with constant `K`; let `g` be another map uniformly
 `C`-close to `f`. If `x` and `y` are their fixed points, then `dist x y ≤ C / (1 - K)`. -/
 theorem dist_fixedPoint_fixedPoint_of_dist_le' (g : α → α) {x y} (hx : IsFixedPt f x)
@@ -511,34 +349,16 @@ theorem fixedPoint_unique {x} (hx : IsFixedPt f x) : x = fixedPoint f hf :=
 #align contracting_with.fixed_point_unique ContractingWith.fixedPoint_unique
 -/
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.dist_fixed_point_le ContractingWith.dist_fixedPoint_leₓ'. -/
 theorem dist_fixedPoint_le (x) : dist x (fixedPoint f hf) ≤ dist x (f x) / (1 - K) :=
   hf.dist_le_of_fixedPoint x hf.fixedPoint_isFixedPt
 #align contracting_with.dist_fixed_point_le ContractingWith.dist_fixedPoint_le
 
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-Case conversion may be inaccurate. Consider using '#align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_leₓ'. -/
 /-- Aposteriori estimates on the convergence of iterates to the fixed point. -/
 theorem aposteriori_dist_iterate_fixedPoint_le (x n) :
     dist ((f^[n]) x) (fixedPoint f hf) ≤ dist ((f^[n]) x) ((f^[n + 1]) x) / (1 - K) := by
   rw [iterate_succ']; apply hf.dist_fixed_point_le
 #align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_le
 
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-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α) (n : Nat), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α) (n : Nat), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (NNReal.toReal K) n)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K)))
-Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_dist_iterate_fixed_point_le ContractingWith.apriori_dist_iterate_fixedPoint_leₓ'. -/
 theorem apriori_dist_iterate_fixedPoint_le (x n) :
     dist ((f^[n]) x) (fixedPoint f hf) ≤ dist x (f x) * K ^ n / (1 - K) :=
   le_trans (hf.aposteriori_dist_iterate_fixedPoint_le x n) <|
@@ -555,12 +375,6 @@ theorem tendsto_iterate_fixedPoint (x) :
 #align contracting_with.tendsto_iterate_fixed_point ContractingWith.tendsto_iterate_fixedPoint
 -/
 
-/- warning: contracting_with.fixed_point_lipschitz_in_map -> ContractingWith.fixedPoint_lipschitz_in_map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] {g : α -> α} (hg : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K g) {C : Real}, (forall (z : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f z) (g z)) C) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3) (ContractingWith.fixedPoint.{u1} α _inst_1 K g hg _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) C (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] {g : α -> α} (hg : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K g) {C : Real}, (forall (z : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f z) (g z)) C) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3) (ContractingWith.fixedPoint.{u1} α _inst_1 K g hg _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) C (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K))))
-Case conversion may be inaccurate. Consider using '#align contracting_with.fixed_point_lipschitz_in_map ContractingWith.fixedPoint_lipschitz_in_mapₓ'. -/
 theorem fixedPoint_lipschitz_in_map {g : α → α} (hg : ContractingWith K g) {C}
     (hfg : ∀ z, dist (f z) (g z) ≤ C) : dist (fixedPoint f hf) (fixedPoint g hg) ≤ C / (1 - K) :=
   hf.dist_fixedPoint_fixedPoint_of_dist_le' g hf.fixedPoint_isFixedPt hg.fixedPoint_isFixedPt hfg

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

@@ -86,10 +86,7 @@ lean 3 declaration is
 but is expected to have type
   forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_topₓ'. -/
-theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ :=
-  by
-  norm_cast
-  exact ENNReal.coe_ne_top
+theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ := by norm_cast; exact ENNReal.coe_ne_top
 #align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_top
 
 /- warning: contracting_with.edist_inequality -> ContractingWith.edist_inequality is a dubious translation:
@@ -230,10 +227,8 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_leₓ'. -/
 theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
-    edist x (efixedPoint f hf x hx) ≤ edist x (f x) / (1 - K) :=
-  by
-  convert hf.apriori_edist_iterate_efixed_point_le hx 0
-  simp only [pow_zero, mul_one]
+    edist x (efixedPoint f hf x hx) ≤ edist x (f x) / (1 - K) := by
+  convert hf.apriori_edist_iterate_efixed_point_le hx 0; simp only [pow_zero, mul_one]
 #align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_le
 
 /- warning: contracting_with.edist_efixed_point_lt_top -> ContractingWith.edist_efixedPoint_lt_top is a dubious translation:
@@ -262,9 +257,7 @@ theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx :
       (hf.eq_or_edist_eq_top_of_fixed_points _ _).elim id fun h' => False.elim (ne_of_lt _ h') <;>
     try apply efixed_point_is_fixed_pt
   change edist_lt_top_setoid.rel _ _
-  trans x;
-  · symm
-    exact hf.edist_efixed_point_lt_top hx
+  trans x; · symm; exact hf.edist_efixed_point_lt_top hx
   trans y
   exacts[lt_top_iff_ne_top.2 h, hf.edist_efixed_point_lt_top hy]
 #align contracting_with.efixed_point_eq_of_edist_lt_top ContractingWith.efixedPoint_eq_of_edist_lt_top
@@ -285,8 +278,7 @@ theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s
   haveI := hsc.complete_space_coe
   rcases hf.exists_fixed_point ⟨x, hxs⟩ hx with ⟨y, hfy, h_tendsto, hle⟩
   refine' ⟨y, y.2, Subtype.ext_iff_val.1 hfy, _, fun n => _⟩
-  · convert(continuous_subtype_coe.tendsto _).comp h_tendsto
-    ext n
+  · convert(continuous_subtype_coe.tendsto _).comp h_tendsto; ext n
     simp only [(· ∘ ·), maps_to.iterate_restrict, maps_to.coe_restrict_apply, Subtype.coe_mk]
   · convert hle n
     rw [maps_to.iterate_restrict, eq_comm, maps_to.coe_restrict_apply, Subtype.coe_mk]
@@ -408,9 +400,7 @@ theorem efixedPoint_eq_of_edist_lt_top' (hf : ContractingWith K f) {s : Set α}
       (hf.eq_or_edist_eq_top_of_fixed_points _ _).elim id fun h' => False.elim (ne_of_lt _ h') <;>
     try apply efixed_point_is_fixed_pt'
   change edist_lt_top_setoid.rel _ _
-  trans x;
-  · symm
-    apply edist_efixed_point_lt_top'
+  trans x; · symm; apply edist_efixed_point_lt_top'
   trans y
   exact lt_top_iff_ne_top.2 hxy
   apply edist_efixed_point_lt_top'
@@ -539,10 +529,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_leₓ'. -/
 /-- Aposteriori estimates on the convergence of iterates to the fixed point. -/
 theorem aposteriori_dist_iterate_fixedPoint_le (x n) :
-    dist ((f^[n]) x) (fixedPoint f hf) ≤ dist ((f^[n]) x) ((f^[n + 1]) x) / (1 - K) :=
-  by
-  rw [iterate_succ']
-  apply hf.dist_fixed_point_le
+    dist ((f^[n]) x) (fixedPoint f hf) ≤ dist ((f^[n]) x) ((f^[n + 1]) x) / (1 - K) := by
+  rw [iterate_succ']; apply hf.dist_fixed_point_le
 #align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_le
 
 /- warning: contracting_with.apriori_dist_iterate_fixed_point_le -> ContractingWith.apriori_dist_iterate_fixedPoint_le is a dubious translation:

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

@@ -272,10 +272,7 @@ theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx :
 omit cs
 
 /- warning: contracting_with.exists_fixed_point' -> ContractingWith.exists_fixedPoint' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))))
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point' ContractingWith.exists_fixedPoint'ₓ'. -/
 /-- Banach fixed-point theorem for maps contracting on a complete subset. -/
 theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
@@ -392,10 +389,7 @@ theorem edist_efixedPoint_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : MapsT
 #align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixedPoint_lt_top'
 
 /- warning: contracting_with.efixed_point_eq_of_edist_lt_top' -> ContractingWith.efixedPoint_eq_of_edist_lt_top' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_eq_of_edist_lt_top' ContractingWith.efixedPoint_eq_of_edist_lt_top'ₓ'. -/
 /-- If a globally contracting map `f` has two complete forward-invariant sets `s`, `t`,
 and `x ∈ s` is at a finite distance from `y ∈ t`, then the `efixed_point'` constructed by `x`

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

@@ -63,7 +63,7 @@ theorem toLipschitzWith (hf : ContractingWith K f) : LipschitzWith K f :=
 
 /- warning: contracting_with.one_sub_K_pos' -> ContractingWith.one_sub_K_pos' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'ₓ'. -/
@@ -94,7 +94,7 @@ theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ :=
 
 /- warning: contracting_with.edist_inequality -> ContractingWith.edist_inequality is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_inequality ContractingWith.edist_inequalityₓ'. -/
@@ -112,7 +112,7 @@ theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞
 
 /- warning: contracting_with.edist_le_of_fixed_point -> ContractingWith.edist_le_of_fixedPoint is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixedPointₓ'. -/
@@ -147,7 +147,7 @@ include cs
 
 /- warning: contracting_with.exists_fixed_point -> ContractingWith.exists_fixedPoint is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point ContractingWith.exists_fixedPointₓ'. -/
@@ -213,7 +213,7 @@ theorem tendsto_iterate_efixedPoint (hf : ContractingWith K f) {x : α} (hx : ed
 
 /- warning: contracting_with.apriori_edist_iterate_efixed_point_le -> ContractingWith.apriori_edist_iterate_efixedPoint_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_leₓ'. -/
@@ -225,7 +225,7 @@ theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
 
 /- warning: contracting_with.edist_efixed_point_le -> ContractingWith.edist_efixedPoint_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_leₓ'. -/
@@ -238,7 +238,7 @@ theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (
 
 /- warning: contracting_with.edist_efixed_point_lt_top -> ContractingWith.edist_efixedPoint_lt_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_lt_top ContractingWith.edist_efixedPoint_lt_topₓ'. -/
@@ -273,7 +273,7 @@ omit cs
 
 /- warning: contracting_with.exists_fixed_point' -> ContractingWith.exists_fixedPoint' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point' ContractingWith.exists_fixedPoint'ₓ'. -/
@@ -353,7 +353,7 @@ theorem tendsto_iterate_efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : Ma
 
 /- warning: contracting_with.apriori_edist_iterate_efixed_point_le' -> ContractingWith.apriori_edist_iterate_efixedPoint_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'ₓ'. -/
@@ -366,7 +366,7 @@ theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s)
 
 /- warning: contracting_with.edist_efixed_point_le' -> ContractingWith.edist_efixedPoint_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixedPoint_le'ₓ'. -/
@@ -380,7 +380,7 @@ theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f
 
 /- warning: contracting_with.edist_efixed_point_lt_top' -> ContractingWith.edist_efixedPoint_lt_top' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixedPoint_lt_top'ₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -65,7 +65,7 @@ theorem toLipschitzWith (hf : ContractingWith K f) : LipschitzWith K f :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'ₓ'. -/
 theorem one_sub_K_pos' (hf : ContractingWith K f) : (0 : ℝ≥0∞) < 1 - K := by simp [hf.1]
 #align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'
@@ -74,7 +74,7 @@ theorem one_sub_K_pos' (hf : ContractingWith K f) : (0 : ℝ≥0∞) < 1 - K :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_ne_zero ContractingWith.one_sub_K_ne_zeroₓ'. -/
 theorem one_sub_K_ne_zero (hf : ContractingWith K f) : (1 : ℝ≥0∞) - K ≠ 0 :=
   ne_of_gt hf.one_sub_K_pos'
@@ -84,7 +84,7 @@ theorem one_sub_K_ne_zero (hf : ContractingWith K f) : (1 : ℝ≥0∞) - K ≠
 lean 3 declaration is
   forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
 but is expected to have type
-  forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+  forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_topₓ'. -/
 theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ :=
   by
@@ -96,7 +96,7 @@ theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_inequality ContractingWith.edist_inequalityₓ'. -/
 theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞) :
     edist x y ≤ (edist x (f x) + edist y (f y)) / (1 - K) :=
@@ -114,7 +114,7 @@ theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixedPointₓ'. -/
 theorem edist_le_of_fixedPoint (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞)
     (hy : IsFixedPt f y) : edist x y ≤ edist x (f x) / (1 - K) := by
@@ -149,7 +149,7 @@ include cs
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point ContractingWith.exists_fixedPointₓ'. -/
 /-- Banach fixed-point theorem, contraction mapping theorem, `emetric_space` version.
 A contracting map on a complete metric space has a fixed point.
@@ -215,7 +215,7 @@ theorem tendsto_iterate_efixedPoint (hf : ContractingWith K f) {x : α} (hx : ed
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_leₓ'. -/
 theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
     (hx : edist x (f x) ≠ ∞) (n : ℕ) :
@@ -227,7 +227,7 @@ theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_leₓ'. -/
 theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) ≤ edist x (f x) / (1 - K) :=
@@ -275,7 +275,7 @@ omit cs
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))))
 Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point' ContractingWith.exists_fixedPoint'ₓ'. -/
 /-- Banach fixed-point theorem for maps contracting on a complete subset. -/
 theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
@@ -355,7 +355,7 @@ theorem tendsto_iterate_efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : Ma
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'ₓ'. -/
 theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞)
@@ -368,7 +368,7 @@ theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s)
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
 Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixedPoint_le'ₓ'. -/
 theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :

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

@@ -327,17 +327,17 @@ theorem efixedPoint_mem' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).fst
 #align contracting_with.efixed_point_mem' ContractingWith.efixedPoint_mem'
 
-/- warning: contracting_with.efixed_point_is_fixed_pt' -> ContractingWith.efixedPoint_is_fixed_pt' is a dubious translation:
+/- warning: contracting_with.efixed_point_is_fixed_pt' -> ContractingWith.efixedPoint_isFixedPt' is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), Function.IsFixedPt.{u1} α f (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), Function.IsFixedPt.{u1} α f (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)
-Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_is_fixed_pt'ₓ'. -/
-theorem efixedPoint_is_fixed_pt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_isFixedPt'ₓ'. -/
+theorem efixedPoint_isFixedPt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint' f hsc hsf hf x hxs hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.1
-#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_is_fixed_pt'
+#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_isFixedPt'
 
 /- warning: contracting_with.tendsto_iterate_efixed_point' -> ContractingWith.tendsto_iterate_efixedPoint' is a dubious translation:
 lean 3 declaration is

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.metric_space.contracting
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Dynamics.FixedPoints.Topology
 /-!
 # Contracting maps
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A Lipschitz continuous self-map with Lipschitz constant `K < 1` is called a *contracting map*.
 In this file we prove the Banach fixed point theorem, some explicit estimates on the rate
 of convergence, and some properties of the map sending a contracting map to its fixed point.

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -39,10 +39,12 @@ open Filter Function
 
 variable {α : Type _}
 
+#print ContractingWith /-
 /-- A map is said to be `contracting_with K`, if `K < 1` and `f` is `lipschitz_with K`. -/
 def ContractingWith [EMetricSpace α] (K : ℝ≥0) (f : α → α) :=
   K < 1 ∧ LipschitzWith K f
 #align contracting_with ContractingWith
+-/
 
 namespace ContractingWith
 
@@ -50,23 +52,49 @@ variable [EMetricSpace α] [cs : CompleteSpace α] {K : ℝ≥0} {f : α → α}
 
 open Emetric Set
 
-theorem to_lipschitzWith (hf : ContractingWith K f) : LipschitzWith K f :=
+#print ContractingWith.toLipschitzWith /-
+theorem toLipschitzWith (hf : ContractingWith K f) : LipschitzWith K f :=
   hf.2
-#align contracting_with.to_lipschitz_with ContractingWith.to_lipschitzWith
+#align contracting_with.to_lipschitz_with ContractingWith.toLipschitzWith
+-/
 
+/- warning: contracting_with.one_sub_K_pos' -> ContractingWith.one_sub_K_pos' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'ₓ'. -/
 theorem one_sub_K_pos' (hf : ContractingWith K f) : (0 : ℝ≥0∞) < 1 - K := by simp [hf.1]
 #align contracting_with.one_sub_K_pos' ContractingWith.one_sub_K_pos'
 
+/- warning: contracting_with.one_sub_K_ne_zero -> ContractingWith.one_sub_K_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_ne_zero ContractingWith.one_sub_K_ne_zeroₓ'. -/
 theorem one_sub_K_ne_zero (hf : ContractingWith K f) : (1 : ℝ≥0∞) - K ≠ 0 :=
   ne_of_gt hf.one_sub_K_pos'
 #align contracting_with.one_sub_K_ne_zero ContractingWith.one_sub_K_ne_zero
 
+/- warning: contracting_with.one_sub_K_ne_top -> ContractingWith.one_sub_K_ne_top is a dubious translation:
+lean 3 declaration is
+  forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {K : NNReal}, Ne.{1} ENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_topₓ'. -/
 theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ :=
   by
   norm_cast
   exact ENNReal.coe_ne_top
 #align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_top
 
+/- warning: contracting_with.edist_inequality -> ContractingWith.edist_inequality is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.edist_inequality ContractingWith.edist_inequalityₓ'. -/
 theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞) :
     edist x y ≤ (edist x (f x) + edist y (f y)) / (1 - K) :=
   suffices edist x y ≤ edist x (f x) + edist y (f y) + K * edist x y by
@@ -79,75 +107,125 @@ theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞
     
 #align contracting_with.edist_inequality ContractingWith.edist_inequality
 
-theorem edist_le_of_fixed_point (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞)
+/- warning: contracting_with.edist_le_of_fixed_point -> ContractingWith.edist_le_of_fixedPoint is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixedPointₓ'. -/
+theorem edist_le_of_fixedPoint (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞)
     (hy : IsFixedPt f y) : edist x y ≤ edist x (f x) / (1 - K) := by
   simpa only [hy.eq, edist_self, add_zero] using hf.edist_inequality h
-#align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixed_point
-
-theorem eq_or_edist_eq_top_of_fixed_points (hf : ContractingWith K f) {x y} (hx : IsFixedPt f x)
+#align contracting_with.edist_le_of_fixed_point ContractingWith.edist_le_of_fixedPoint
+
+/- warning: contracting_with.eq_or_edist_eq_top_of_fixed_points -> ContractingWith.eq_or_edist_eq_top_of_fixedPoints is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Function.IsFixedPt.{u1} α f x) -> (Function.IsFixedPt.{u1} α f y) -> (Or (Eq.{succ u1} α x y) (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {x : α} {y : α}, (Function.IsFixedPt.{u1} α f x) -> (Function.IsFixedPt.{u1} α f y) -> (Or (Eq.{succ u1} α x y) (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.eq_or_edist_eq_top_of_fixed_points ContractingWith.eq_or_edist_eq_top_of_fixedPointsₓ'. -/
+theorem eq_or_edist_eq_top_of_fixedPoints (hf : ContractingWith K f) {x y} (hx : IsFixedPt f x)
     (hy : IsFixedPt f y) : x = y ∨ edist x y = ∞ :=
   by
   refine' or_iff_not_imp_right.2 fun h => edist_le_zero.1 _
   simpa only [hx.eq, edist_self, add_zero, ENNReal.zero_div] using hf.edist_le_of_fixed_point h hy
-#align contracting_with.eq_or_edist_eq_top_of_fixed_points ContractingWith.eq_or_edist_eq_top_of_fixed_points
+#align contracting_with.eq_or_edist_eq_top_of_fixed_points ContractingWith.eq_or_edist_eq_top_of_fixedPoints
 
+#print ContractingWith.restrict /-
 /-- If a map `f` is `contracting_with K`, and `s` is a forward-invariant set, then
 restriction of `f` to `s` is `contracting_with K` as well. -/
 theorem restrict (hf : ContractingWith K f) {s : Set α} (hs : MapsTo f s s) :
     ContractingWith K (hs.restrict f s s) :=
   ⟨hf.1, fun x y => hf.2 x y⟩
 #align contracting_with.restrict ContractingWith.restrict
+-/
 
 include cs
 
+/- warning: contracting_with.exists_fixed_point -> ContractingWith.exists_fixedPoint is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point ContractingWith.exists_fixedPointₓ'. -/
 /-- Banach fixed-point theorem, contraction mapping theorem, `emetric_space` version.
 A contracting map on a complete metric space has a fixed point.
 We include more conclusions in this theorem to avoid proving them again later.
 
 The main API for this theorem are the functions `efixed_point` and `fixed_point`,
 and lemmas about these functions. -/
-theorem exists_fixed_point (hf : ContractingWith K f) (x : α) (hx : edist x (f x) ≠ ∞) :
+theorem exists_fixedPoint (hf : ContractingWith K f) (x : α) (hx : edist x (f x) ≠ ∞) :
     ∃ y,
       IsFixedPt f y ∧
         Tendsto (fun n => (f^[n]) x) atTop (𝓝 y) ∧
           ∀ n : ℕ, edist ((f^[n]) x) y ≤ edist x (f x) * K ^ n / (1 - K) :=
   have : CauchySeq fun n => (f^[n]) x :=
     cauchySeq_of_edist_le_geometric K (edist x (f x)) (ENNReal.coe_lt_one_iff.2 hf.1) hx
-      (hf.to_lipschitzWith.edist_iterate_succ_le_geometric x)
+      (hf.toLipschitzWith.edist_iterate_succ_le_geometric x)
   let ⟨y, hy⟩ := cauchySeq_tendsto_of_complete this
   ⟨y, isFixedPt_of_tendsto_iterate hy hf.2.Continuous.ContinuousAt, hy,
     edist_le_of_edist_le_geometric_of_tendsto K (edist x (f x))
-      (hf.to_lipschitzWith.edist_iterate_succ_le_geometric x) hy⟩
-#align contracting_with.exists_fixed_point ContractingWith.exists_fixed_point
+      (hf.toLipschitzWith.edist_iterate_succ_le_geometric x) hy⟩
+#align contracting_with.exists_fixed_point ContractingWith.exists_fixedPoint
 
 variable (f)
 
+/- warning: contracting_with.efixed_point -> ContractingWith.efixedPoint is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} (f : α -> α), (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> α)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} (f : α -> α), (ContractingWith.{u1} α _inst_1 K f) -> (forall (x : α), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> α)
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point ContractingWith.efixedPointₓ'. -/
 -- avoid `efixed_point _` in pretty printer
 /-- Let `x` be a point of a complete emetric space. Suppose that `f` is a contracting map,
 and `edist x (f x) ≠ ∞`. Then `efixed_point` is the unique fixed point of `f`
 in `emetric.ball x ∞`. -/
 noncomputable def efixedPoint (hf : ContractingWith K f) (x : α) (hx : edist x (f x) ≠ ∞) : α :=
-  Classical.choose <| hf.exists_fixed_point x hx
+  Classical.choose <| hf.exists_fixedPoint x hx
 #align contracting_with.efixed_point ContractingWith.efixedPoint
 
 variable {f}
 
+/- warning: contracting_with.efixed_point_is_fixed_pt -> ContractingWith.efixedPoint_isFixedPt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), Function.IsFixedPt.{u1} α f (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), Function.IsFixedPt.{u1} α f (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_is_fixed_pt ContractingWith.efixedPoint_isFixedPtₓ'. -/
 theorem efixedPoint_isFixedPt (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint f hf x hx) :=
-  (Classical.choose_spec <| hf.exists_fixed_point x hx).1
+  (Classical.choose_spec <| hf.exists_fixedPoint x hx).1
 #align contracting_with.efixed_point_is_fixed_pt ContractingWith.efixedPoint_isFixedPt
 
+/- warning: contracting_with.tendsto_iterate_efixed_point -> ContractingWith.tendsto_iterate_efixedPoint is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx))
+Case conversion may be inaccurate. Consider using '#align contracting_with.tendsto_iterate_efixed_point ContractingWith.tendsto_iterate_efixedPointₓ'. -/
 theorem tendsto_iterate_efixedPoint (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     Tendsto (fun n => (f^[n]) x) atTop (𝓝 <| efixedPoint f hf x hx) :=
-  (Classical.choose_spec <| hf.exists_fixed_point x hx).2.1
+  (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.1
 #align contracting_with.tendsto_iterate_efixed_point ContractingWith.tendsto_iterate_efixedPoint
 
+/- warning: contracting_with.apriori_edist_iterate_efixed_point_le -> ContractingWith.apriori_edist_iterate_efixedPoint_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_leₓ'. -/
 theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
     (hx : edist x (f x) ≠ ∞) (n : ℕ) :
     edist ((f^[n]) x) (efixedPoint f hf x hx) ≤ edist x (f x) * K ^ n / (1 - K) :=
-  (Classical.choose_spec <| hf.exists_fixed_point x hx).2.2 n
+  (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.2 n
 #align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_le
 
+/- warning: contracting_with.edist_efixed_point_le -> ContractingWith.edist_efixedPoint_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_leₓ'. -/
 theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) ≤ edist x (f x) / (1 - K) :=
   by
@@ -155,12 +233,24 @@ theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (
   simp only [pow_zero, mul_one]
 #align contracting_with.edist_efixed_point_le ContractingWith.edist_efixedPoint_le
 
+/- warning: contracting_with.edist_efixed_point_lt_top -> ContractingWith.edist_efixedPoint_lt_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_lt_top ContractingWith.edist_efixedPoint_lt_topₓ'. -/
 theorem edist_efixedPoint_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) < ∞ :=
   (hf.edist_efixedPoint_le hx).trans_lt
     (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
 #align contracting_with.edist_efixed_point_lt_top ContractingWith.edist_efixedPoint_lt_top
 
+/- warning: contracting_with.efixed_point_eq_of_edist_lt_top -> ContractingWith.efixedPoint_eq_of_edist_lt_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) {y : α} (hy : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Eq.{succ u1} α (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf y hy))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] [cs : CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α _inst_1 K f) {x : α} (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) {y : α} (hy : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) y (f y)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Eq.{succ u1} α (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf x hx) (ContractingWith.efixedPoint.{u1} α _inst_1 cs K f hf y hy))
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_eq_of_edist_lt_top ContractingWith.efixedPoint_eq_of_edist_lt_topₓ'. -/
 theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞)
     {y : α} (hy : edist y (f y) ≠ ∞) (h : edist x y ≠ ∞) :
     efixedPoint f hf x hx = efixedPoint f hf y hy :=
@@ -178,8 +268,14 @@ theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx :
 
 omit cs
 
+/- warning: contracting_with.exists_fixed_point' -> ContractingWith.exists_fixedPoint' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K))))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (And (Function.IsFixedPt.{u1} α f y) (And (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) y)) (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) y) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K))))))))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.exists_fixed_point' ContractingWith.exists_fixedPoint'ₓ'. -/
 /-- Banach fixed-point theorem for maps contracting on a complete subset. -/
-theorem exists_fixed_point' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     ∃ y ∈ s,
       IsFixedPt f y ∧
@@ -194,10 +290,16 @@ theorem exists_fixed_point' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s
     simp only [(· ∘ ·), maps_to.iterate_restrict, maps_to.coe_restrict_apply, Subtype.coe_mk]
   · convert hle n
     rw [maps_to.iterate_restrict, eq_comm, maps_to.coe_restrict_apply, Subtype.coe_mk]
-#align contracting_with.exists_fixed_point' ContractingWith.exists_fixed_point'
+#align contracting_with.exists_fixed_point' ContractingWith.exists_fixedPoint'
 
 variable (f)
 
+/- warning: contracting_with.efixed_point' -> ContractingWith.efixedPoint' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} (f : α -> α) {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> α))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} (f : α -> α) {s : Set.{u1} α}, (IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) -> (forall (hsf : Set.MapsTo.{u1, u1} α α f s s), (ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> α))
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point' ContractingWith.efixedPoint'ₓ'. -/
 -- avoid `efixed_point _` in pretty printer
 /-- Let `s` be a complete forward-invariant set of a self-map `f`. If `f` contracts on `s`
 and `x ∈ s` satisfies `edist x (f x) ≠ ∞`, then `efixed_point'` is the unique fixed point
@@ -205,58 +307,100 @@ of the restriction of `f` to `s ∩ emetric.ball x ∞`. -/
 noncomputable def efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) (x : α) (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     α :=
-  Classical.choose <| hf.exists_fixed_point' hsc hsf hxs hx
+  Classical.choose <| hf.exists_fixedPoint' hsc hsf hxs hx
 #align contracting_with.efixed_point' ContractingWith.efixedPoint'
 
 variable {f}
 
-theorem efixed_point_mem' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+/- warning: contracting_with.efixed_point_mem' -> ContractingWith.efixedPoint_mem' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx) s
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx) s
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_mem' ContractingWith.efixedPoint_mem'ₓ'. -/
+theorem efixedPoint_mem' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     efixedPoint' f hsc hsf hf x hxs hx ∈ s :=
-  (Classical.choose_spec <| hf.exists_fixed_point' hsc hsf hxs hx).fst
-#align contracting_with.efixed_point_mem' ContractingWith.efixed_point_mem'
-
-theorem efixed_point_is_fixed_pt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+  (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).fst
+#align contracting_with.efixed_point_mem' ContractingWith.efixedPoint_mem'
+
+/- warning: contracting_with.efixed_point_is_fixed_pt' -> ContractingWith.efixedPoint_is_fixed_pt' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), Function.IsFixedPt.{u1} α f (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), Function.IsFixedPt.{u1} α f (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_is_fixed_pt'ₓ'. -/
+theorem efixedPoint_is_fixed_pt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint' f hsc hsf hf x hxs hx) :=
-  (Classical.choose_spec <| hf.exists_fixed_point' hsc hsf hxs hx).snd.1
-#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixed_point_is_fixed_pt'
-
+  (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.1
+#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_is_fixed_pt'
+
+/- warning: contracting_with.tendsto_iterate_efixed_point' -> ContractingWith.tendsto_iterate_efixedPoint' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1))) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => Nat.iterate.{succ u1} α f n x) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1))) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx))
+Case conversion may be inaccurate. Consider using '#align contracting_with.tendsto_iterate_efixed_point' ContractingWith.tendsto_iterate_efixedPoint'ₓ'. -/
 theorem tendsto_iterate_efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     Tendsto (fun n => (f^[n]) x) atTop (𝓝 <| efixedPoint' f hsc hsf hf x hxs hx) :=
-  (Classical.choose_spec <| hf.exists_fixed_point' hsc hsf hxs hx).snd.2.1
+  (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.2.1
 #align contracting_with.tendsto_iterate_efixed_point' ContractingWith.tendsto_iterate_efixedPoint'
 
-theorem apriori_edist_iterate_efixed_point_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+/- warning: contracting_with.apriori_edist_iterate_efixed_point_le' -> ContractingWith.apriori_edist_iterate_efixedPoint_le' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (ENNReal.some K) n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'ₓ'. -/
+theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞)
     (n : ℕ) :
     edist ((f^[n]) x) (efixedPoint' f hsc hsf hf x hxs hx) ≤ edist x (f x) * K ^ n / (1 - K) :=
-  (Classical.choose_spec <| hf.exists_fixed_point' hsc hsf hxs hx).snd.2.2 n
-#align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixed_point_le'
-
-theorem edist_efixed_point_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+  (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).snd.2.2 n
+#align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'
+
+/- warning: contracting_with.edist_efixed_point_le' -> ContractingWith.edist_efixedPoint_le' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (ENNReal.some K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixedPoint_le'ₓ'. -/
+theorem edist_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) ≤ edist x (f x) / (1 - K) :=
   by
   convert hf.apriori_edist_iterate_efixed_point_le' hsc hsf hxs hx 0
   rw [pow_zero, mul_one]
-#align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixed_point_le'
-
-theorem edist_efixed_point_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+#align contracting_with.edist_efixed_point_le' ContractingWith.edist_efixedPoint_le'
+
+/- warning: contracting_with.edist_efixed_point_lt_top' -> ContractingWith.edist_efixedPoint_lt_top' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α} {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hf : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hf x hxs hx)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixedPoint_lt_top'ₓ'. -/
+theorem edist_efixedPoint_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) < ∞ :=
-  (hf.edist_efixed_point_le' hsc hsf hxs hx).trans_lt
+  (hf.edist_efixedPoint_le' hsc hsf hxs hx).trans_lt
     (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
-#align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixed_point_lt_top'
-
+#align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixedPoint_lt_top'
+
+/- warning: contracting_with.efixed_point_eq_of_edist_lt_top' -> ContractingWith.efixedPoint_eq_of_edist_lt_top' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hfs : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) {t : Set.{u1} α} (htc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) t) (htf : Set.MapsTo.{u1, u1} α α f t t) (hft : ContractingWith.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) t) (Subtype.emetricSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f t t htf)) {y : α} (hyt : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (hy : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) y (f y)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Eq.{succ u1} α (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hfs x hxs hx) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f t htc htf hft y hyt hy)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α _inst_1 K f) -> (forall {s : Set.{u1} α} (hsc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (hsf : Set.MapsTo.{u1, u1} α α f s s) (hfs : ContractingWith.{u1} (Set.Elem.{u1} α s) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f s s hsf)) {x : α} (hxs : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (hx : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x (f x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) {t : Set.{u1} α} (htc : IsComplete.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) t) (htf : Set.MapsTo.{u1, u1} α α f t t) (hft : ContractingWith.{u1} (Set.Elem.{u1} α t) (instEMetricSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) _inst_1) K (Set.MapsTo.restrict.{u1, u1} α α f t t htf)) {y : α} (hyt : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (hy : Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) y (f y)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))), (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Eq.{succ u1} α (ContractingWith.efixedPoint'.{u1} α _inst_1 K f s hsc hsf hfs x hxs hx) (ContractingWith.efixedPoint'.{u1} α _inst_1 K f t htc htf hft y hyt hy)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.efixed_point_eq_of_edist_lt_top' ContractingWith.efixedPoint_eq_of_edist_lt_top'ₓ'. -/
 /-- If a globally contracting map `f` has two complete forward-invariant sets `s`, `t`,
 and `x ∈ s` is at a finite distance from `y ∈ t`, then the `efixed_point'` constructed by `x`
 is the same as the `efixed_point'` constructed by `y`.
 
 This lemma takes additional arguments stating that `f` contracts on `s` and `t` because this way
 it can be used to prove the desired equality with non-trivial proofs of these facts. -/
-theorem efixed_point_eq_of_edist_lt_top' (hf : ContractingWith K f) {s : Set α} (hsc : IsComplete s)
+theorem efixedPoint_eq_of_edist_lt_top' (hf : ContractingWith K f) {s : Set α} (hsc : IsComplete s)
     (hsf : MapsTo f s s) (hfs : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s)
     (hx : edist x (f x) ≠ ∞) {t : Set α} (htc : IsComplete t) (htf : MapsTo f t t)
     (hft : ContractingWith K <| htf.restrict f t t) {y : α} (hyt : y ∈ t) (hy : edist y (f y) ≠ ∞)
@@ -273,7 +417,7 @@ theorem efixed_point_eq_of_edist_lt_top' (hf : ContractingWith K f) {s : Set α}
   trans y
   exact lt_top_iff_ne_top.2 hxy
   apply edist_efixed_point_lt_top'
-#align contracting_with.efixed_point_eq_of_edist_lt_top' ContractingWith.efixed_point_eq_of_edist_lt_top'
+#align contracting_with.efixed_point_eq_of_edist_lt_top' ContractingWith.efixedPoint_eq_of_edist_lt_top'
 
 end ContractingWith
 
@@ -283,14 +427,32 @@ variable [MetricSpace α] {K : ℝ≥0} {f : α → α} (hf : ContractingWith K
 
 include hf
 
+/- warning: contracting_with.one_sub_K_pos -> ContractingWith.one_sub_K_pos is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.one_sub_K_pos ContractingWith.one_sub_K_posₓ'. -/
 theorem one_sub_K_pos (hf : ContractingWith K f) : (0 : ℝ) < 1 - K :=
   sub_pos.2 hf.1
 #align contracting_with.one_sub_K_pos ContractingWith.one_sub_K_pos
 
+/- warning: contracting_with.dist_le_mul -> ContractingWith.dist_le_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) (y : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) (y : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f x) (f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (NNReal.toReal K) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.dist_le_mul ContractingWith.dist_le_mulₓ'. -/
 theorem dist_le_mul (x y : α) : dist (f x) (f y) ≤ K * dist x y :=
-  hf.to_lipschitzWith.dist_le_mul x y
+  hf.toLipschitzWith.dist_le_mul x y
 #align contracting_with.dist_le_mul ContractingWith.dist_le_mul
 
+/- warning: contracting_with.dist_inequality -> ContractingWith.dist_inequality is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) (y : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) (y : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) y (f y))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.dist_inequality ContractingWith.dist_inequalityₓ'. -/
 theorem dist_inequality (x y) : dist x y ≤ (dist x (f x) + dist y (f y)) / (1 - K) :=
   suffices dist x y ≤ dist x (f x) + dist y (f y) + K * dist x y by
     rwa [le_div_iff hf.one_sub_K_pos, mul_comm, sub_mul, one_mul, sub_le_iff_le_add]
@@ -300,25 +462,39 @@ theorem dist_inequality (x y) : dist x y ≤ (dist x (f x) + dist y (f y)) / (1
     
 #align contracting_with.dist_inequality ContractingWith.dist_inequality
 
-theorem dist_le_of_fixed_point (x) {y} (hy : IsFixedPt f y) : dist x y ≤ dist x (f x) / (1 - K) :=
-  by simpa only [hy.eq, dist_self, add_zero] using hf.dist_inequality x y
-#align contracting_with.dist_le_of_fixed_point ContractingWith.dist_le_of_fixed_point
-
-theorem fixed_point_unique' {x y} (hx : IsFixedPt f x) (hy : IsFixedPt f y) : x = y :=
-  (hf.eq_or_edist_eq_top_of_fixed_points hx hy).resolve_right (edist_ne_top _ _)
-#align contracting_with.fixed_point_unique' ContractingWith.fixed_point_unique'
+/- warning: contracting_with.dist_le_of_fixed_point -> ContractingWith.dist_le_of_fixedPoint is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) {y : α}, (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (x : α) {y : α}, (Function.IsFixedPt.{u1} α f y) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K)))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.dist_le_of_fixed_point ContractingWith.dist_le_of_fixedPointₓ'. -/
+theorem dist_le_of_fixedPoint (x) {y} (hy : IsFixedPt f y) : dist x y ≤ dist x (f x) / (1 - K) := by
+  simpa only [hy.eq, dist_self, add_zero] using hf.dist_inequality x y
+#align contracting_with.dist_le_of_fixed_point ContractingWith.dist_le_of_fixedPoint
+
+#print ContractingWith.fixedPoint_unique' /-
+theorem fixedPoint_unique' {x y} (hx : IsFixedPt f x) (hy : IsFixedPt f y) : x = y :=
+  (hf.eq_or_edist_eq_top_of_fixedPoints hx hy).resolve_right (edist_ne_top _ _)
+#align contracting_with.fixed_point_unique' ContractingWith.fixedPoint_unique'
+-/
 
+/- warning: contracting_with.dist_fixed_point_fixed_point_of_dist_le' -> ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (g : α -> α) {x : α} {y : α}, (Function.IsFixedPt.{u1} α f x) -> (Function.IsFixedPt.{u1} α g y) -> (forall {C : Real}, (forall (z : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f z) (g z)) C) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) C (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α}, (ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) -> (forall (g : α -> α) {x : α} {y : α}, (Function.IsFixedPt.{u1} α f x) -> (Function.IsFixedPt.{u1} α g y) -> (forall {C : Real}, (forall (z : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f z) (g z)) C) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) C (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K))))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le'ₓ'. -/
 /-- Let `f` be a contracting map with constant `K`; let `g` be another map uniformly
 `C`-close to `f`. If `x` and `y` are their fixed points, then `dist x y ≤ C / (1 - K)`. -/
-theorem dist_fixed_point_fixed_point_of_dist_le' (g : α → α) {x y} (hx : IsFixedPt f x)
+theorem dist_fixedPoint_fixedPoint_of_dist_le' (g : α → α) {x y} (hx : IsFixedPt f x)
     (hy : IsFixedPt g y) {C} (hfg : ∀ z, dist (f z) (g z) ≤ C) : dist x y ≤ C / (1 - K) :=
   calc
     dist x y = dist y x := dist_comm x y
-    _ ≤ dist y (f y) / (1 - K) := (hf.dist_le_of_fixed_point y hx)
+    _ ≤ dist y (f y) / (1 - K) := (hf.dist_le_of_fixedPoint y hx)
     _ = dist (f y) (g y) / (1 - K) := by rw [hy.eq, dist_comm]
     _ ≤ C / (1 - K) := (div_le_div_right hf.one_sub_K_pos).2 (hfg y)
     
-#align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixed_point_fixed_point_of_dist_le'
+#align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le'
 
 noncomputable section
 
@@ -326,26 +502,44 @@ variable [Nonempty α] [CompleteSpace α]
 
 variable (f)
 
+#print ContractingWith.fixedPoint /-
 /-- The unique fixed point of a contracting map in a nonempty complete metric space. -/
 def fixedPoint : α :=
   efixedPoint f hf _ (edist_ne_top (Classical.choice ‹Nonempty α›) _)
 #align contracting_with.fixed_point ContractingWith.fixedPoint
+-/
 
 variable {f}
 
+#print ContractingWith.fixedPoint_isFixedPt /-
 /-- The point provided by `contracting_with.fixed_point` is actually a fixed point. -/
 theorem fixedPoint_isFixedPt : IsFixedPt f (fixedPoint f hf) :=
   hf.efixedPoint_isFixedPt _
 #align contracting_with.fixed_point_is_fixed_pt ContractingWith.fixedPoint_isFixedPt
+-/
 
+#print ContractingWith.fixedPoint_unique /-
 theorem fixedPoint_unique {x} (hx : IsFixedPt f x) : x = fixedPoint f hf :=
-  hf.fixed_point_unique' hx hf.fixedPoint_isFixedPt
+  hf.fixedPoint_unique' hx hf.fixedPoint_isFixedPt
 #align contracting_with.fixed_point_unique ContractingWith.fixedPoint_unique
+-/
 
+/- warning: contracting_with.dist_fixed_point_le -> ContractingWith.dist_fixedPoint_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.dist_fixed_point_le ContractingWith.dist_fixedPoint_leₓ'. -/
 theorem dist_fixedPoint_le (x) : dist x (fixedPoint f hf) ≤ dist x (f x) / (1 - K) :=
-  hf.dist_le_of_fixed_point x hf.fixedPoint_isFixedPt
+  hf.dist_le_of_fixedPoint x hf.fixedPoint_isFixedPt
 #align contracting_with.dist_fixed_point_le ContractingWith.dist_fixedPoint_le
 
+/- warning: contracting_with.aposteriori_dist_iterate_fixed_point_le -> ContractingWith.aposteriori_dist_iterate_fixedPoint_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α) (n : Nat), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (Nat.iterate.{succ u1} α f (HAdd.hAdd.{0, 0, 0} Nat 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)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α) (n : Nat), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (Nat.iterate.{succ u1} α f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_leₓ'. -/
 /-- Aposteriori estimates on the convergence of iterates to the fixed point. -/
 theorem aposteriori_dist_iterate_fixedPoint_le (x n) :
     dist ((f^[n]) x) (fixedPoint f hf) ≤ dist ((f^[n]) x) ((f^[n + 1]) x) / (1 - K) :=
@@ -354,12 +548,19 @@ theorem aposteriori_dist_iterate_fixedPoint_le (x n) :
   apply hf.dist_fixed_point_le
 #align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_le
 
+/- warning: contracting_with.apriori_dist_iterate_fixed_point_le -> ContractingWith.apriori_dist_iterate_fixedPoint_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α) (n : Nat), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K) n)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] (x : α) (n : Nat), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (Nat.iterate.{succ u1} α f n x) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x (f x)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (NNReal.toReal K) n)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K)))
+Case conversion may be inaccurate. Consider using '#align contracting_with.apriori_dist_iterate_fixed_point_le ContractingWith.apriori_dist_iterate_fixedPoint_leₓ'. -/
 theorem apriori_dist_iterate_fixedPoint_le (x n) :
     dist ((f^[n]) x) (fixedPoint f hf) ≤ dist x (f x) * K ^ n / (1 - K) :=
   le_trans (hf.aposteriori_dist_iterate_fixedPoint_le x n) <|
-    (div_le_div_right hf.one_sub_K_pos).2 <| hf.to_lipschitzWith.dist_iterate_succ_le_geometric x n
+    (div_le_div_right hf.one_sub_K_pos).2 <| hf.toLipschitzWith.dist_iterate_succ_le_geometric x n
 #align contracting_with.apriori_dist_iterate_fixed_point_le ContractingWith.apriori_dist_iterate_fixedPoint_le
 
+#print ContractingWith.tendsto_iterate_fixedPoint /-
 theorem tendsto_iterate_fixedPoint (x) :
     Tendsto (fun n => (f^[n]) x) atTop (𝓝 <| fixedPoint f hf) :=
   by
@@ -367,14 +568,22 @@ theorem tendsto_iterate_fixedPoint (x) :
   refine' (fixed_point_unique _ _).symm
   apply efixed_point_is_fixed_pt
 #align contracting_with.tendsto_iterate_fixed_point ContractingWith.tendsto_iterate_fixedPoint
+-/
 
+/- warning: contracting_with.fixed_point_lipschitz_in_map -> ContractingWith.fixedPoint_lipschitz_in_map is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] {g : α -> α} (hg : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K g) {C : Real}, (forall (z : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f z) (g z)) C) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3) (ContractingWith.fixedPoint.{u1} α _inst_1 K g hg _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) C (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal Real (HasLiftT.mk.{1, 1} NNReal Real (CoeTCₓ.coe.{1, 1} NNReal Real (coeBase.{1, 1} NNReal Real NNReal.Real.hasCoe))) K))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {K : NNReal} {f : α -> α} (hf : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K f) [_inst_2 : Nonempty.{succ u1} α] [_inst_3 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))] {g : α -> α} (hg : ContractingWith.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1) K g) {C : Real}, (forall (z : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (f z) (g z)) C) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) (ContractingWith.fixedPoint.{u1} α _inst_1 K f hf _inst_2 _inst_3) (ContractingWith.fixedPoint.{u1} α _inst_1 K g hg _inst_2 _inst_3)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) C (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (NNReal.toReal K))))
+Case conversion may be inaccurate. Consider using '#align contracting_with.fixed_point_lipschitz_in_map ContractingWith.fixedPoint_lipschitz_in_mapₓ'. -/
 theorem fixedPoint_lipschitz_in_map {g : α → α} (hg : ContractingWith K g) {C}
     (hfg : ∀ z, dist (f z) (g z) ≤ C) : dist (fixedPoint f hf) (fixedPoint g hg) ≤ C / (1 - K) :=
-  hf.dist_fixed_point_fixed_point_of_dist_le' g hf.fixedPoint_isFixedPt hg.fixedPoint_isFixedPt hfg
+  hf.dist_fixedPoint_fixedPoint_of_dist_le' g hf.fixedPoint_isFixedPt hg.fixedPoint_isFixedPt hfg
 #align contracting_with.fixed_point_lipschitz_in_map ContractingWith.fixedPoint_lipschitz_in_map
 
 omit hf
 
+#print ContractingWith.isFixedPt_fixedPoint_iterate /-
 /-- If a map `f` has a contracting iterate `f^[n]`, then the fixed point of `f^[n]` is also a fixed
 point of `f`. -/
 theorem isFixedPt_fixedPoint_iterate {n : ℕ} (hf : ContractingWith K (f^[n])) :
@@ -388,6 +597,7 @@ theorem isFixedPt_fixedPoint_iterate {n : ℕ} (hf : ContractingWith K (f^[n]))
   have := dist_pos.2 (Ne.symm this)
   simpa only [NNReal.coe_one, one_mul, NNReal.val_eq_coe] using (mul_lt_mul_right this).mpr hf.left
 #align contracting_with.is_fixed_pt_fixed_point_iterate ContractingWith.isFixedPt_fixedPoint_iterate
+-/
 
 end ContractingWith
 

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

@@ -189,7 +189,7 @@ theorem exists_fixed_point' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s
   haveI := hsc.complete_space_coe
   rcases hf.exists_fixed_point ⟨x, hxs⟩ hx with ⟨y, hfy, h_tendsto, hle⟩
   refine' ⟨y, y.2, Subtype.ext_iff_val.1 hfy, _, fun n => _⟩
-  · convert (continuous_subtype_coe.tendsto _).comp h_tendsto
+  · convert(continuous_subtype_coe.tendsto _).comp h_tendsto
     ext n
     simp only [(· ∘ ·), maps_to.iterate_restrict, maps_to.coe_restrict_apply, Subtype.coe_mk]
   · convert hle n

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -40,13 +40,13 @@ open Filter Function
 variable {α : Type _}
 
 /-- A map is said to be `contracting_with K`, if `K < 1` and `f` is `lipschitz_with K`. -/
-def ContractingWith [EmetricSpace α] (K : ℝ≥0) (f : α → α) :=
+def ContractingWith [EMetricSpace α] (K : ℝ≥0) (f : α → α) :=
   K < 1 ∧ LipschitzWith K f
 #align contracting_with ContractingWith
 
 namespace ContractingWith
 
-variable [EmetricSpace α] [cs : CompleteSpace α] {K : ℝ≥0} {f : α → α}
+variable [EMetricSpace α] [cs : CompleteSpace α] {K : ℝ≥0} {f : α → α}
 
 open Emetric Set
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -314,7 +314,7 @@ theorem dist_fixed_point_fixed_point_of_dist_le' (g : α → α) {x y} (hx : IsF
     (hy : IsFixedPt g y) {C} (hfg : ∀ z, dist (f z) (g z) ≤ C) : dist x y ≤ C / (1 - K) :=
   calc
     dist x y = dist y x := dist_comm x y
-    _ ≤ dist y (f y) / (1 - K) := hf.dist_le_of_fixed_point y hx
+    _ ≤ dist y (f y) / (1 - K) := (hf.dist_le_of_fixed_point y hx)
     _ = dist (f y) (g y) / (1 - K) := by rw [hy.eq, dist_comm]
     _ ≤ C / (1 - K) := (div_le_div_right hf.one_sub_K_pos).2 (hfg y)
     

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -33,7 +33,7 @@ contracting map, fixed point, Banach fixed point theorem
 -/
 
 
-open NNReal Topology Classical Ennreal
+open NNReal Topology Classical ENNReal
 
 open Filter Function
 
@@ -64,14 +64,14 @@ theorem one_sub_K_ne_zero (hf : ContractingWith K f) : (1 : ℝ≥0∞) - K ≠
 theorem one_sub_K_ne_top : (1 : ℝ≥0∞) - K ≠ ∞ :=
   by
   norm_cast
-  exact Ennreal.coe_ne_top
+  exact ENNReal.coe_ne_top
 #align contracting_with.one_sub_K_ne_top ContractingWith.one_sub_K_ne_top
 
 theorem edist_inequality (hf : ContractingWith K f) {x y} (h : edist x y ≠ ∞) :
     edist x y ≤ (edist x (f x) + edist y (f y)) / (1 - K) :=
   suffices edist x y ≤ edist x (f x) + edist y (f y) + K * edist x y by
-    rwa [Ennreal.le_div_iff_mul_le (Or.inl hf.one_sub_K_ne_zero) (Or.inl one_sub_K_ne_top),
-      mul_comm, Ennreal.sub_mul fun _ _ => h, one_mul, tsub_le_iff_right]
+    rwa [ENNReal.le_div_iff_mul_le (Or.inl hf.one_sub_K_ne_zero) (Or.inl one_sub_K_ne_top),
+      mul_comm, ENNReal.sub_mul fun _ _ => h, one_mul, tsub_le_iff_right]
   calc
     edist x y ≤ edist x (f x) + edist (f x) (f y) + edist (f y) y := edist_triangle4 _ _ _ _
     _ = edist x (f x) + edist y (f y) + edist (f x) (f y) := by rw [edist_comm y, add_right_comm]
@@ -88,7 +88,7 @@ theorem eq_or_edist_eq_top_of_fixed_points (hf : ContractingWith K f) {x y} (hx
     (hy : IsFixedPt f y) : x = y ∨ edist x y = ∞ :=
   by
   refine' or_iff_not_imp_right.2 fun h => edist_le_zero.1 _
-  simpa only [hx.eq, edist_self, add_zero, Ennreal.zero_div] using hf.edist_le_of_fixed_point h hy
+  simpa only [hx.eq, edist_self, add_zero, ENNReal.zero_div] using hf.edist_le_of_fixed_point h hy
 #align contracting_with.eq_or_edist_eq_top_of_fixed_points ContractingWith.eq_or_edist_eq_top_of_fixed_points
 
 /-- If a map `f` is `contracting_with K`, and `s` is a forward-invariant set, then
@@ -112,7 +112,7 @@ theorem exists_fixed_point (hf : ContractingWith K f) (x : α) (hx : edist x (f
         Tendsto (fun n => (f^[n]) x) atTop (𝓝 y) ∧
           ∀ n : ℕ, edist ((f^[n]) x) y ≤ edist x (f x) * K ^ n / (1 - K) :=
   have : CauchySeq fun n => (f^[n]) x :=
-    cauchySeq_of_edist_le_geometric K (edist x (f x)) (Ennreal.coe_lt_one_iff.2 hf.1) hx
+    cauchySeq_of_edist_le_geometric K (edist x (f x)) (ENNReal.coe_lt_one_iff.2 hf.1) hx
       (hf.to_lipschitzWith.edist_iterate_succ_le_geometric x)
   let ⟨y, hy⟩ := cauchySeq_tendsto_of_complete this
   ⟨y, isFixedPt_of_tendsto_iterate hy hf.2.Continuous.ContinuousAt, hy,
@@ -158,7 +158,7 @@ theorem edist_efixedPoint_le (hf : ContractingWith K f) {x : α} (hx : edist x (
 theorem edist_efixedPoint_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint f hf x hx) < ∞ :=
   (hf.edist_efixedPoint_le hx).trans_lt
-    (Ennreal.mul_lt_top hx <| Ennreal.inv_ne_top.2 hf.one_sub_K_ne_zero)
+    (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
 #align contracting_with.edist_efixed_point_lt_top ContractingWith.edist_efixedPoint_lt_top
 
 theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞)
@@ -247,7 +247,7 @@ theorem edist_efixed_point_lt_top' {s : Set α} (hsc : IsComplete s) (hsf : Maps
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     edist x (efixedPoint' f hsc hsf hf x hxs hx) < ∞ :=
   (hf.edist_efixed_point_le' hsc hsf hxs hx).trans_lt
-    (Ennreal.mul_lt_top hx <| Ennreal.inv_ne_top.2 hf.one_sub_K_ne_zero)
+    (ENNReal.mul_lt_top hx <| ENNReal.inv_ne_top.2 hf.one_sub_K_ne_zero)
 #align contracting_with.edist_efixed_point_lt_top' ContractingWith.edist_efixed_point_lt_top'
 
 /-- If a globally contracting map `f` has two complete forward-invariant sets `s`, `t`,

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

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -294,7 +294,7 @@ theorem dist_fixedPoint_fixedPoint_of_dist_le' (g : α → α) {x y} (hx : IsFix
     (hy : IsFixedPt g y) {C} (hfg : ∀ z, dist (f z) (g z) ≤ C) : dist x y ≤ C / (1 - K) :=
   calc
     dist x y = dist y x := dist_comm x y
-    _ ≤ dist y (f y) / (1 - K) := (hf.dist_le_of_fixedPoint y hx)
+    _ ≤ dist y (f y) / (1 - K) := hf.dist_le_of_fixedPoint y hx
     _ = dist (f y) (g y) / (1 - K) := by rw [hy.eq, dist_comm]
     _ ≤ C / (1 - K) := (div_le_div_right hf.one_sub_K_pos).2 (hfg y)
 #align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le'

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -300,7 +300,6 @@ theorem dist_fixedPoint_fixedPoint_of_dist_le' (g : α → α) {x y} (hx : IsFix
 #align contracting_with.dist_fixed_point_fixed_point_of_dist_le' ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le'
 
 variable [Nonempty α] [CompleteSpace α]
-
 variable (f)
 
 /-- The unique fixed point of a contracting map in a nonempty complete metric space. -/

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -31,7 +31,8 @@ contracting map, fixed point, Banach fixed point theorem
 -/
 
 
-open NNReal Topology Classical ENNReal Filter Function
+open scoped Classical
+open NNReal Topology ENNReal Filter Function
 
 variable {α : Type*}
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -6,6 +6,7 @@ Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudr
 import Mathlib.Analysis.SpecificLimits.Basic
 import Mathlib.Data.Setoid.Basic
 import Mathlib.Dynamics.FixedPoints.Topology
+import Mathlib.Topology.MetricSpace.Lipschitz
 
 #align_import topology.metric_space.contracting from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -32,7 +32,7 @@ contracting map, fixed point, Banach fixed point theorem
 
 open NNReal Topology Classical ENNReal Filter Function
 
-variable {α : Type _}
+variable {α : Type*}
 
 /-- A map is said to be `ContractingWith K`, if `K < 1` and `f` is `LipschitzWith K`. -/
 def ContractingWith [EMetricSpace α] (K : ℝ≥0) (f : α → α) :=

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Rohan Mitta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.metric_space.contracting
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecificLimits.Basic
 import Mathlib.Data.Setoid.Basic
 import Mathlib.Dynamics.FixedPoints.Topology
 
+#align_import topology.metric_space.contracting from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Contracting maps
 

@@ -102,9 +102,9 @@ We include more conclusions in this theorem to avoid proving them again later.
 The main API for this theorem are the functions `efixedPoint` and `fixedPoint`,
 and lemmas about these functions. -/
 theorem exists_fixedPoint (hf : ContractingWith K f) (x : α) (hx : edist x (f x) ≠ ∞) :
-    ∃ y, IsFixedPt f y ∧ Tendsto (fun n ↦ (f^[n]) x) atTop (𝓝 y) ∧
-      ∀ n : ℕ, edist ((f^[n]) x) y ≤ edist x (f x) * (K : ℝ≥0∞) ^ n / (1 - K) :=
-  have : CauchySeq fun n ↦ (f^[n]) x :=
+    ∃ y, IsFixedPt f y ∧ Tendsto (fun n ↦ f^[n] x) atTop (𝓝 y) ∧
+      ∀ n : ℕ, edist (f^[n] x) y ≤ edist x (f x) * (K : ℝ≥0∞) ^ n / (1 - K) :=
+  have : CauchySeq fun n ↦ f^[n] x :=
     cauchySeq_of_edist_le_geometric K (edist x (f x)) (ENNReal.coe_lt_one_iff.2 hf.1) hx
       (hf.toLipschitzWith.edist_iterate_succ_le_geometric x)
   let ⟨y, hy⟩ := cauchySeq_tendsto_of_complete this
@@ -131,13 +131,13 @@ theorem efixedPoint_isFixedPt (hf : ContractingWith K f) {x : α} (hx : edist x
 #align contracting_with.efixed_point_is_fixed_pt ContractingWith.efixedPoint_isFixedPt
 
 theorem tendsto_iterate_efixedPoint (hf : ContractingWith K f) {x : α} (hx : edist x (f x) ≠ ∞) :
-    Tendsto (fun n ↦ (f^[n]) x) atTop (𝓝 <| efixedPoint f hf x hx) :=
+    Tendsto (fun n ↦ f^[n] x) atTop (𝓝 <| efixedPoint f hf x hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.1
 #align contracting_with.tendsto_iterate_efixed_point ContractingWith.tendsto_iterate_efixedPoint
 
 theorem apriori_edist_iterate_efixedPoint_le (hf : ContractingWith K f) {x : α}
     (hx : edist x (f x) ≠ ∞) (n : ℕ) :
-    edist ((f^[n]) x) (efixedPoint f hf x hx) ≤ edist x (f x) * (K : ℝ≥0∞) ^ n / (1 - K) :=
+    edist (f^[n] x) (efixedPoint f hf x hx) ≤ edist x (f x) * (K : ℝ≥0∞) ^ n / (1 - K) :=
   (Classical.choose_spec <| hf.exists_fixedPoint x hx).2.2 n
 #align contracting_with.apriori_edist_iterate_efixed_point_le ContractingWith.apriori_edist_iterate_efixedPoint_le
 
@@ -169,8 +169,8 @@ theorem efixedPoint_eq_of_edist_lt_top (hf : ContractingWith K f) {x : α} (hx :
 /-- Banach fixed-point theorem for maps contracting on a complete subset. -/
 theorem exists_fixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
-    ∃ y ∈ s, IsFixedPt f y ∧ Tendsto (fun n ↦ (f^[n]) x) atTop (𝓝 y) ∧
-      ∀ n : ℕ, edist ((f^[n]) x) y ≤ edist x (f x) * (K : ℝ≥0∞) ^ n / (1 - K) := by
+    ∃ y ∈ s, IsFixedPt f y ∧ Tendsto (fun n ↦ f^[n] x) atTop (𝓝 y) ∧
+      ∀ n : ℕ, edist (f^[n] x) y ≤ edist x (f x) * (K : ℝ≥0∞) ^ n / (1 - K) := by
   haveI := hsc.completeSpace_coe
   rcases hf.exists_fixedPoint ⟨x, hxs⟩ hx with ⟨y, hfy, h_tendsto, hle⟩
   refine' ⟨y, y.2, Subtype.ext_iff_val.1 hfy, _, fun n ↦ _⟩
@@ -209,14 +209,14 @@ theorem efixedPoint_isFixedPt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f
 
 theorem tendsto_iterate_efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
-    Tendsto (fun n ↦ (f^[n]) x) atTop (𝓝 <| efixedPoint' f hsc hsf hf x hxs hx) :=
+    Tendsto (fun n ↦ f^[n] x) atTop (𝓝 <| efixedPoint' f hsc hsf hf x hxs hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).2.2.1
 #align contracting_with.tendsto_iterate_efixed_point' ContractingWith.tendsto_iterate_efixedPoint'
 
 theorem apriori_edist_iterate_efixedPoint_le' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞)
     (n : ℕ) :
-    edist ((f^[n]) x) (efixedPoint' f hsc hsf hf x hxs hx) ≤
+    edist (f^[n] x) (efixedPoint' f hsc hsf hf x hxs hx) ≤
       edist x (f x) * (K : ℝ≥0∞) ^ n / (1 - K) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).2.2.2 n
 #align contracting_with.apriori_edist_iterate_efixed_point_le' ContractingWith.apriori_edist_iterate_efixedPoint_le'
@@ -326,19 +326,19 @@ theorem dist_fixedPoint_le (x) : dist x (fixedPoint f hf) ≤ dist x (f x) / (1
 
 /-- Aposteriori estimates on the convergence of iterates to the fixed point. -/
 theorem aposteriori_dist_iterate_fixedPoint_le (x n) :
-    dist ((f^[n]) x) (fixedPoint f hf) ≤ dist ((f^[n]) x) ((f^[n + 1]) x) / (1 - K) := by
+    dist (f^[n] x) (fixedPoint f hf) ≤ dist (f^[n] x) (f^[n + 1] x) / (1 - K) := by
   rw [iterate_succ']
   apply hf.dist_fixedPoint_le
 #align contracting_with.aposteriori_dist_iterate_fixed_point_le ContractingWith.aposteriori_dist_iterate_fixedPoint_le
 
 theorem apriori_dist_iterate_fixedPoint_le (x n) :
-    dist ((f^[n]) x) (fixedPoint f hf) ≤ dist x (f x) * (K : ℝ) ^ n / (1 - K) :=
+    dist (f^[n] x) (fixedPoint f hf) ≤ dist x (f x) * (K : ℝ) ^ n / (1 - K) :=
   le_trans (hf.aposteriori_dist_iterate_fixedPoint_le x n) <|
     (div_le_div_right hf.one_sub_K_pos).2 <| hf.toLipschitzWith.dist_iterate_succ_le_geometric x n
 #align contracting_with.apriori_dist_iterate_fixed_point_le ContractingWith.apriori_dist_iterate_fixedPoint_le
 
 theorem tendsto_iterate_fixedPoint (x) :
-    Tendsto (fun n ↦ (f^[n]) x) atTop (𝓝 <| fixedPoint f hf) := by
+    Tendsto (fun n ↦ f^[n] x) atTop (𝓝 <| fixedPoint f hf) := by
   convert tendsto_iterate_efixedPoint hf (edist_ne_top x _)
   refine' (fixedPoint_unique _ _).symm
   apply efixedPoint_isFixedPt
@@ -351,10 +351,10 @@ theorem fixedPoint_lipschitz_in_map {g : α → α} (hg : ContractingWith K g) {
 
 /-- If a map `f` has a contracting iterate `f^[n]`, then the fixed point of `f^[n]` is also a fixed
 point of `f`. -/
-theorem isFixedPt_fixedPoint_iterate {n : ℕ} (hf : ContractingWith K (f^[n])) :
-    IsFixedPt f (hf.fixedPoint (f^[n])) := by
-  set x := hf.fixedPoint (f^[n])
-  have hx : (f^[n]) x = x := hf.fixedPoint_isFixedPt
+theorem isFixedPt_fixedPoint_iterate {n : ℕ} (hf : ContractingWith K f^[n]) :
+    IsFixedPt f (hf.fixedPoint f^[n]) := by
+  set x := hf.fixedPoint f^[n]
+  have hx : f^[n] x = x := hf.fixedPoint_isFixedPt
   have := hf.toLipschitzWith.dist_le_mul x (f x)
   rw [← iterate_succ_apply, iterate_succ_apply', hx] at this
   -- Porting note: Originally `contrapose! this`

@@ -33,9 +33,7 @@ contracting map, fixed point, Banach fixed point theorem
 -/
 
 
-open NNReal Topology Classical ENNReal
-
-open Filter Function
+open NNReal Topology Classical ENNReal Filter Function
 
 variable {α : Type _}
 
@@ -203,11 +201,11 @@ theorem efixedPoint_mem' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).1
 #align contracting_with.efixed_point_mem' ContractingWith.efixedPoint_mem'
 
-theorem efixedPoint_is_fixed_pt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
+theorem efixedPoint_isFixedPt' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
     IsFixedPt f (efixedPoint' f hsc hsf hf x hxs hx) :=
   (Classical.choose_spec <| hf.exists_fixedPoint' hsc hsf hxs hx).2.1
-#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_is_fixed_pt'
+#align contracting_with.efixed_point_is_fixed_pt' ContractingWith.efixedPoint_isFixedPt'
 
 theorem tendsto_iterate_efixedPoint' {s : Set α} (hsc : IsComplete s) (hsf : MapsTo f s s)
     (hf : ContractingWith K <| hsf.restrict f s s) {x : α} (hxs : x ∈ s) (hx : edist x (f x) ≠ ∞) :
@@ -250,7 +248,7 @@ theorem efixedPoint_eq_of_edist_lt_top' (hf : ContractingWith K f) {s : Set α}
     (hxy : edist x y ≠ ∞) :
     efixedPoint' f hsc hsf hfs x hxs hx = efixedPoint' f htc htf hft y hyt hy := by
   refine' (hf.eq_or_edist_eq_top_of_fixedPoints _ _).elim id fun h' ↦ False.elim (ne_of_lt _ h')
-    <;> try apply efixedPoint_is_fixed_pt'
+    <;> try apply efixedPoint_isFixedPt'
   change edistLtTopSetoid.Rel _ _
   trans x
   · apply Setoid.symm' -- Porting note: Originally `symm`

Co-authored-by: Moritz Firsching <firsching@google.com>